For many years, the interest at WIAS concerning the modeling of semiconductor devices was focused to classical models like the driftdiffusion model, its analysis and numerical implementation. The model was augmented by including optical fields (laser and photovoltaic modeling), device temperature (energy models) and other effects.
However, in the last 20 years the typical length scale of semiconductor devices has moved from microns to a few nanometers. This has the consequences that quantum effects become more and more important. Hence for the WIAS this yields the natural task to follow this development in modeling. In particular this means, to move from classical modeling to a quantum mechanical description of semiconductor devices. Since the existing classical models are very successful and since a pure quantum description is in fact impossible one follows the strategy at WIAS, to find models which combine the advantages of classical modeling with the accuracy of quantum description.
Multiscale modeling
Following this hybrid strategy one uses a classical driftdiffusion model in regions, where quantum effects can be neglected, and a quantum description in regions, where quantum effects (for instance tunneling and resonances) are important for the understanding of the physical processes going on. Both descriptions have to be combine in a suitable manner. For the quantum description this leads to the problem to handle open quantum systems which is closely related to the problem of transparent boundary conditions. Typical examples of such semiconductor devices are nanowires (nanowiretransistors, resonanttunneling diodes etc.), embedded quantum dots, lasers and optoelectronic devices (LEDs, VCSELs, solar cells etc.).From the mathematical point of view one has to verify the correctness of hybrid models and their solvability. The concept was implemented in 1D for a simple driftdiffusion model without generation and recombination. In view of nanowire devices efforts have been made to carry over the concept from 1D to 2D and 3D. The basic tool for the quantum description is an open SchrödingerPoisson system. One has to point out that closed SchrödingerPoisson systems were intensively studied at WIAS in the past. Lasers and optoelectronic devices require to include optical fields into the hybrid modeling which leads to new mathematical challenges.
Publications
Monographs

S. Rodt, P.I. Schneider, L. Zschiedrich, T. Heindel, S. Bounouar, M. Kantner, Th. Koprucki, U. Bandelow, S. Burger, S. Reitzenstein, Chapter 8: Deterministic Quantum Devices for Optical Quantum Communication, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in SolidState Sciences, Springer, Heidelberg, 2020, pp. 285359, (Chapter Published), DOI 10.1007/9783030356569_8 .
Abstract
Photonic quantum technologies are based on the exchange of information via single photons. The information is typically encoded in the polarization of the photons and security is ensured intrinsically via principles of quantum mechanics such as the nocloning theorem. Thus, all optical quantum communication networks rely crucially on the availability of suitable quantumlight sources. Such light sources with close to ideal optical and quantum optical properties can be realized by selfassembled semiconductor quantum dots. These highquality nanocrystals are predestined singlephoton emitters due to their quasi zerodimensional carrier confinement. Still, the development of practical quantumdotbased sources of single photons and entangledphoton pairs for applications in photonic quantum technology and especially for the quantumrepeater scheme is very demanding and requires highly advanced device concepts and deterministic fabrication technologies. This is mainly explained by their random position and emission energy as well as by the low photonextraction efficiency in simple planar device configurations. 
M. Kantner, Th. Höhne, Th. Koprucki, S. Burger, H.J. Wünsche, F. Schmidt, A. Mielke, U. Bandelow, Chapter 7: MultiDimensional Modeling and Simulation of Semiconductor Nanophotonic Devices, in: Semiconductor Nanophotonics, M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann, eds., 194 of Springer Series in SolidState Sciences, Springer, Heidelberg, 2020, pp. 241283, (Chapter Published), DOI 10.1007/9783030356569_7 .
Abstract
Selfconsistent modeling and multidimensional simulation of semiconductor nanophotonicdevices is an important tool in the development of future integrated light sources and quantumdevices. Simulations can guide important technological decisions by revealing performance bottlenecks in new device concepts, contribute to their understanding and help to theoretically exploretheir optimization potential. The efficient implementation of multidimensional numerical simulationsfor computeraided design tasks requires sophisticated numerical methods and modeling techniques. We review recent advances in devicescale modeling of quantum dot based singlephotonsources and laser diodes by selfconsistently coupling the optical Maxwell equations with semiclassical carrier transport models using semiclassical and fully quantum mechanical descriptionsof the optically active region, respectively. For the simulation of realistic devices with complex,multidimensional geometries, we have developed a novel hpadaptive finite element approachfor the optical Maxwell equations, using mixed meshes adapted to the multiscale properties ofthe photonic structures. For electrically driven devices, we introduced novel discretization andparameterembedding techniques to solve the driftdiffusion system for strongly degenerate semiconductors at cryogenic temperature. Our methodical advances are demonstrated on variousapplications, including verticalcavity surfaceemitting lasers, grating couplers and singlephotonsources. 
P. Exner, W. König, H. Neidhardt, eds., Mathematical Results in Quantum Mechanics. Proceedings of the QMath12 Conference, World Scientific Publishing, Singapore, 2015, xii+383 pages, (Collection Published).

A. Zisowsky, A. Arnold, M. Ehrhardt, Th. Koprucki, Chapter 7: Transient Simulation of k$cdot$pSchrödinger Systems Using Discrete Transparent Boundary Conditions, in: MultiBand Effective Mass Approximations  Advanced Mathematical Models and Numerical Techniques, M. Ehrhardt, Th. Koprucki, eds., 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, pp. 247272, (Chapter Published).

D. Klindworth, M. Ehrhardt, Th. Koprucki, Chapter 8: Discrete Transparent Boundary Conditions for Multiband Effective Mass Approximations, in: MultiBand Effective Mass Approximations  Advanced Mathematical Models and Numerical Techniques, M. Ehrhardt, Th. Koprucki, eds., 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, pp. 273318, (Chapter Published).

M. Ehrhardt, Th. Koprucki, eds., MultiBand Effective Mass Approximations  Advanced Mathematical Models and Numerical Techniques, 94 of Lecture Notes in Computational Science and Engineering, Springer, Cham et al., 2014, xvi+318 pages, (Monograph Published).

A. Mielke, Chapter 21: Dissipative Quantum Mechanics Using GENERIC, in: Recent Trends in Dynamical Systems  Proceedings of a Conference in Honor of Jürgen Scheurle, A. Johann, H.P. Kruse, F. Rupp, S. Schmitz, eds., 35 of Springer Proceedings in Mathematics & Statistics, Springer, Basel et al., 2013, pp. 555585, (Chapter Published).
Abstract
Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework (General Equations for NonEquilibrium Reversible Irreversible Coupling) to construct thermodynamically consistent evolution equations as a sum of a Hamiltonian and a gradientflow contribution, which satisfy a particular noninteraction condition. One of our models couples a quantum system to a finite number of heat baths each of which is described by a timedependent temperature. The dissipation mechanism is modeled via the canonical correlation operator, which is the inverse of the KuboMori metric for density matrices and which is strongly linked to the von Neumann entropy for quantum systems. Thus, one recovers the dissipative doublebracket operators of the Lindblad equations but encounters a correction term for the consistent coupling to the dissipative dynamics. For the finitedimensional and isothermal case we provide a general existence result and discuss sufficient conditions that guarantee that all solutions converge to the unique thermal equilibrium state. Finally, we compare of our gradient flow formulation for quantum systems with the Wasserstein gradient flow formulation for the FokkerPlanck equation and the entropy gradient flow formulation for reversible Markov chains.
Articles in Refereed Journals

D. Chaudhuri, M. O'Donovan, T. Streckenbach, O. Marquart, P. Farrell, S.K. Patra, Th. Koprucki, S. Schulz, Multiscale simulations of the electronic structure of IIInitride quantum wells with varied Indium content: Connecting atomistic and continuumbased models, Journal of Applied Physics, 129 (2021), published online on 18.02.2021, DOI 10.1063/5.0031514 .

A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, Th. Koprucki, Numerical simulation of TEM images for In(Ga)As/GaAs quantum dots with various shapes, Optical and Quantum Electronics, 52 (2020), pp. 257/1257/11, DOI 10.1007/s1108202002356y .
Abstract
We present a mathematical model and a tool chain for the numerical simulation of TEM images of semiconductor quantum dots (QDs). This includes elasticity theory to obtain the strain profile coupled with the DarwinHowieWhelan equations, describing the propagation of the electron wave through the sample. We perform a simulation study on indium gallium arsenide QDs with different shapes and compare the resulting TEM images to experimental ones. This tool chain can be applied to generate a database of simulated TEM images, which is a key element of a novel concept for modelbased geometry reconstruction of semiconductor QDs, involving machine learning techniques. 
O. Marquardt, M.A. Caro, Th. Koprucki, P. Mathé, M. Willatzen, Multiband k $cdot$ p model and fitting scheme for ab initiobased electronic structure parameters for wurtzite GaAs, Phys. Rev. B., 101 (2020), pp. 235147/1235147/12, DOI 10.1103/PhysRevB.101.235147 .
Abstract
We develop a 16band k · p model for the description of wurtzite GaAs, together with a novel scheme to determine electronic structure parameters for multiband k · p models. Our approach uses lowdiscrepancy sequences to fit k · p band structures beyond the eightband scheme to most recent ab initio data, obtained within the framework for hybridfunctional density functional theory with a screenedexchange hybrid functional. We report structural parameters, elastic constants, band structures along highsymmetry lines, and deformation potentials at the Γ point. Based on this, we compute the bulk electronic properties (Γ point energies, effective masses, Luttingerlike parameters, and optical matrix parameters) for a tenband and a sixteenband k · p model for wurtzite GaAs. Our fitting scheme can assign priorities to both selected bands and k points that are of particular interest for specific applications. Finally, ellipticity conditions can be taken into account within our fitting scheme in order to make the resulting parameter sets robust against spurious solutions. 
J. Lähnemann, M.O. Hill, J. Herranz, O. Marquardt, G. Gao, A. Al Hassan, A. Davtyan, S.O. Hruszkewycz, M.V. Holt, Ch. Huang, I. CalvoAlmazán, U. Jahn, U. Pietsch, L.J. Lauhon, L. Geelhaar, Correlated nanoscale analysis of the emission from wurtzite versus zincblende (In,Ga)As/GaAs nanowire coreshell quantum wells, ACS Nano, 19 (2019), pp. 44484457, DOI 10.1021/acs.nanolett.9b01241 .
Abstract
While the properties of wurtzite GaAs have been extensively studied during the past decade, little is known about the influence of the crystal polytype on ternary (In,Ga)As quantum well structures. We address this question with a unique combination of correlated, spatially resolved measurement techniques on coreshell nanowires that contain extended segments of both the zincblende and wurtzite polytypes. Cathodoluminescence hyperspectral imaging reveals a blueshift of the quantum well emission energy by 75 ± 15 meV in the wurtzite polytype segment. Nanoprobe Xray diffraction and atom probe tomography enable k•p calculations for the specific sample geometry to reveal two comparable contributions to this shift. First, there is a 30% drop in In mole fraction going from the zincblende to the wurtzite segment. Second, the quantum well is under compressive strain, which has a much stronger impact on the hole ground state in the wurtzite than in the zincblende segment. Our results highlight the role of the crystal structure in tuning the emission of (In,Ga)As quantum wells and pave the way to exploit the possibilities of threedimensional band gap engineering in coreshell nanowire heterostructures. At the same time, we have demonstrated an advanced characterization toolkit for the investigation of semiconductor nanostructures. 
M. Kantner, M. Mittnenzweig, Th. Koprucki, Hybrid quantumclassical modeling of quantum dot devices, Phys. Rev. B., 96 (2017), pp. 205301/1205301/17, DOI 10.1103/PhysRevB.96.205301 .
Abstract
The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the wellestablished fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we obtain a new hybrid quantumclassical modeling approach, which enables a comprehensive description of quantum dot devices on multiple scales: It allows the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven singlephoton source based on a single quantum dot in the stationary and transient operation regime. 
A. Boitsev, H. Neidhardt, I.Y. Popov, Dirac operator coupled to bosons, Nanosystems: Physics, Chemistry, Mathematics, 7 (2016), pp. 332339.

H. Neidhardt, L. Wilhelm, V. Zagrebnov, A new model for quantum dot light emittingabsorbing devices: Proofs and supplements, Nanosystems: Physics, Chemistry, Mathematics, 6 (2015), pp. 645.

C. Kreisbeck, L. Mascarenhas, Asymptotic spectral analysis in semiconductor nanowire heterostructures, Applicable Analysis. An International Journal, (published online on June 2, 2014), DOI 10.1080/00036811.2014.919052 .

P. Exner, H. Neidhardt, M. Tatar, V. Zagrebnov, Nonequilibrium current via geometric scatterers, Journal of Physics. A. Mathematical and General, 47 (2014), pp. 395301/1395301/16.

H. Neidhardt, L. Wilhelm, V.A. Zagrebnov, A new model of quantum dot light emittingabsorbing devices, Journal of Mathematical Physics, Analysis, Geometry (MAG), 10 (2014), pp. 137.
Abstract
Motivated by the JaynesCummings (JC) model, we consider here a quantum dot coupled simultaneously to a reservoir of photons and to two electric leads (freefermion reservoirs). This JaynesCummingsLeads (JCL) model makes possible that the fermion current through the dot creates a photon flux, which describes a lightemitting device. The same model is also describe a transformation of the photon flux into current of fermions, i.e. a quantum dot lightabsorbing device. The key tool to obtain these results is an abstract LandauerBüttiker formula. 
P.N. Racec, S. Schade, H.Chr. Kaiser, Eigensolutions of the WignerEisenbud problem for a cylindrical nanowire within finite volume method, Journal of Computational Physics, 252 (2013), pp. 5264.
Abstract
We present a finite volume method for computing a representative range of eigenvalues and eigenvectors of the Schrödinger operator on a three dimensional cylindrically symmetric bounded domain with mixed boundary conditions. More specifically, we deal with a semiconductor nanowire which consists of a dominant host material and contains heterostructure features such as doublebarriers or quantum dots. The three dimensional Schrödinger operator is reduced to a family of two dimensional Schrödinger operators distinguished by a centrifugal potential. Ultimately, we numerically treat them by means of a finite volume method. We consider a uniform, boundary conforming Delaunay mesh, which additionally conforms to the material interfaces. The 1/r singularity is eliminated by approximating r at the vertexes of the Voronoi boxes. We study how the anisotropy of the effective mass tensor acts on the uniform approximation of the first K eigenvalues and eigenvectors and their sequential arrangement. There exists an optimal uniform Delaunay discretization with matching anisotropy. This anisotropic discretization yields best accuracy also in the presence of a mildly varying scattering potential, shown exemplarily for a nanowire resonant tunneling diode. For potentials with 1/r singularity one retrieves the theoretically established first order convergence, while the second order convergence is recovered only on uniform grids with an anisotropy correction. 
J. Giannoulis, A. Mielke, Ch. Sparber, Highfrequency averaging in semiclassical Hartreetype equations, Asymptotic Analysis, 70 (2010), pp. 87100.
Abstract
We investigate the asymptotic behavior of solutions to semiclassical Schröodinger equations with nonlinearities of Hartree type. For a weakly nonlinear scaling, we show the validity of an asymptotic superposition principle for slowly modulated highly oscillatory pulses. The result is based on a highfrequency averaging effect due to the nonlocal nature of the Hartree potential, which inhibits the creation of new resonant waves. In the proof we make use of the framework of Wiener algebras. 
R. Racec, U. Wulf, P.N. Racec, Fano regime of transport through open quantum dots, Phys. Rev. B., 82 (2010), pp. 085313/1085313/16.
Abstract
We analyze a quantum dot strongly coupled to the conducting leads via quantum point contacts  Fano regime of transport  and report a variety of resonant states which demonstrate the dominance of the interacting resonances in the scattering process in a low confining potential. There are resonant states similar to the eigenstates of the isolated dot, whose widths increase with increasing the coupling strength to the environment, and hybrid resonant states. The last ones are approximatively obtained as a linear combination of eigenstates with the same parity in the lateral direction, and the corresponding resonances show the phenomena of resonance trapping or level repulsion. The existence of the hybrid modes suggests that the open quantum dot behaves in the Fano regime like an artificial molecule. 
K. Hoke, H.Chr. Kaiser, J. Rehberg, Analyticity for some operator functions from statistical quantum mechanics, Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics, 10 (2009), pp. 749771.
Abstract
For rather general thermodynamic equilibrium distribution functions the density of a statistical ensemble of quantum mechanical particles depends analytically on the potential in the Schrödinger operator describing the quantum system. A key to the proof is that the resolvent to a power less than one of an elliptic operator with nonsmooth coefficients, and mixed Dirichlet/Neumann boundary conditions on a bounded up to threedimensional Lipschitz domain factorizes over the space of essentially bounded functions. 
P.N. Racec, R. Racec, H. Neidhardt, Evanescent channels and scattering in cylindrical nanowire heterostructures, Phys. Rev. B., 79 (2009), pp. 155305/1155305/14.
Abstract
We investigate the scattering phenomena produced by a general finite range nonseparable potential in a multichannel twoprobe cylindrical nanowire heterostructure. The multichannel current scattering matrix is efficiently computed using the Rmatrix formalism extended for cylindrical coordinates. Considering the contribution of the evanescent channels to the scattering matrix, we are able to put in evidence the specific dips in the tunneling coefficient in the case of an attractive potential. The cylindrical symmetry cancels the ”selection rules” known for Cartesian coordinates. If the attractive potential is superposed over a nonuniform potential along the nanowire, then resonant transmission peaks appear. We can characterize them quantitatively through the poles of the current scattering matrix. Detailed maps of the localization probability density sustain the physical interpretation of the resonances (dips and peaks). Our formalism is applied to a variety of model systems like a quantum dot, a core/shell quantum ring or a double barrier, embedded into the nanocylinder. 
H.D. Cornean, H. Neidhardt, V.A. Zagrebnov, The effect of timedependent coupling on nonequilibrium steady states, Annales Henri Poincare. A Journal of Theoretical and Mathematical Physics, 10 (2009), pp. 6193.
Abstract
Consider (for simplicity) two onedimensional semiinfinite leads coupled to a quantum well via time dependent point interactions. In the remote past the system is decoupled, and each of its components is at thermal equilibrium. In the remote future the system is fully coupled. We define and compute the non equilibrium steady state (NESS) generated by this evolution. We show that when restricted to the subspace of absolute continuity of the fully coupled system, the state does not depend at all on the switching. Moreover, we show that the stationary charge current has the same invariant property, and derive the LandauLifschitz and LandauerBüttiker formulas. 
H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Monotonicity properties of the quantum mechanical particle density: An elementary proof, Monatshefte fur Mathematik, 158 (2009), pp. 179185.
Abstract
An elementary proof of the antimonotonicity of the quantum mechanical particle density with respect to the potential in the Hamiltonian is given for a large class of admissible thermodynamic equilibrium distribution functions. In particular the zero temperature case is included. 
H. Neidhardt, V.A. Zagrebnov, Linear nonautonomous Cauchy problems and evolution semigroups, Advances in Differential Equations, 14 (2009), pp. 289340.
Abstract
The paper is devoted to the problem of existence of propagators for an abstract linear nonautonomous evolution Cauchy problem of hyperbolic type in separable Banach spaces. The problem is solved using the socalled evolution semigroup approach which reduces the existence problem for propagators to a perturbation problem of semigroup generators. The results are specified to abstract linear nonautonomous evolution equations in Hilbert spaces where the assumption is made that the domains of the quadratic forms associated with the generators are independent of time. Finally, these results are applied to timedependent Schrödinger operators with moving point interactions in 1D. 
J.A. Griepentrog, W. Höppner, H.Chr. Kaiser, J. Rehberg, A biLipschitz continuous, volume preserving map from the unit ball onto a cube, Note di Matematica, 28 (2008), pp. 185201.
Abstract
We construct two biLipschitz, volume preserving maps from Euclidean space onto itself which map the unit ball onto a cylinder and onto a cube, respectively. Moreover, we characterize invariant sets of these mappings. 
J. Behrndt, M.M. Malamud, H. Neidhardt, Scattering matrices and Weyl functions, Proceedings of the London Mathematical Society. Third Series, 97 (2008), pp. 568598.
Abstract
For a scattering system consisting of two selfadjoint extensions of a symmetric operator A with finite deficiency indices, the scattering matrix and the spectral shift function are calculated in terms of the Weyl function associated with the boundary triplet for A* and a simple proof of the KreinBirman formula is given. The results are applied to singular SturmLiouville operators with scalar and matrixvalued potentials, to Dirac operators and to Schroedinger operators with point interactions. 
J. Behrndt, H. Neidhardt, R. Racec, P.N. Racec, U. Wulf, On Eisenbud's and Wigner's Rmatrix: A general approach, Journal of Differential Equations, 244 (2008), pp. 25452577.
Abstract
The main objective of this paper is to give a rigorous treatment of Wigner's and Eisenbud's Rmatrix method for scattering matrices of scattering systems consisting of two selfadjoint extensions of the same symmetric operator with finite deficiency indices. In the framework of boundary triplets and associated Weyl functions an abstract generalization of the Rmatrix method is developed and the results are applied to Schrödinger operators on the real axis. 
H. Cornean, K. Hoke, H. Neidhardt, P.N. Racec, J. Rehberg, A KohnSham system at zero temperature, Journal of Physics. A. Mathematical and General, 41 (2008), pp. 385304/1385304/21.
Abstract
An onedimensional KohnSham system for spin particles is considered which effectively describes semiconductor nanostructures and which is investigated at zero temperature. We prove the existence of solutions and derive a priori estimates. For this purpose we find estimates for eigenvalues of the Schrödinger operator with effective KohnSham potential and obtain $W^1,2$bounds of the associated particle density operator. Afterwards, compactness and continuity results allow to apply Schauder's fixed point theorem. In case of vanishing exchangecorrelation potential uniqueness is shown by monotonicity arguments. Finally, we investigate the behavior of the system if the temperature approaches zero. 
J. Giannoulis, A. Mielke, Ch. Sparber, Interaction of modulated pulses in the nonlinear Schrödinger equation with periodic potential, Journal of Differential Equations, 245 (2008), pp. 939963.
Abstract
We consider a cubic nonlinear Schrödinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic dynamics of these pulses. 
R. HallerDintelmann, H.Chr. Kaiser, J. Rehberg, Elliptic model problems including mixed boundary conditions and material heterogeneities, Journal de Mathématiques Pures et Appliquées, 89 (2008), pp. 2548.

J. Behrndt, M.M. Malamud, H. Neidhardt, Scattering theory for open quantum systems with finite rank coupling, Mathematical Physics, Analysis and Geometry. An International Journal Devoted to the Theory and Applications of Analysis and Geometry to Physics, 10 (2007), pp. 313358.
Abstract
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or socalled PseudoHamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator $A_D$ in a Hilbert space $sH$ is used to describe an open quantum system. In this case the minimal selfadjoint dilation $widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed system which contains the open system $[A_D,sH]$, but since $widetilde K$ is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family $[A(mu)]$ of maximal dissipative operators depending on energy $mu$, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single PseudoHamiltonians as in the first part of the paper. The general results are applied to a class of SturmLiouville operators arising in dissipative and quantum transmitting SchrödingerPoisson systems. 
J. Even, F. Doré, C. Cornet, L. Pedesseau, A. Schliwa, D. Bimberg, Semianalytical evaluation of linear and nonlinear piezoelectric potentials for quantum nanostructures with axial symmetry, Applied Physics Letters, 91 (2007), pp. 122112/1122112/3.

A. Marent, M. Geller, A. Schliwa, D. Feise, K. Pötschke, D. Bimberg, N. Akcay, N. Öncan, 10$^6$ years extrapolated hole storage time in GaSb/AlAs quantum dots, Applied Physics Letters, 91 (2007), pp. 242109/1242109/3.

V. Mlinar, A. Schliwa, D. Bimberg, F.M. Peeters, Theoretical study of electronic and optical properties of inverted GaAs/AlGaAs quantum dots with smoothed interfaces in an external magnetic field, Phys. Rev. B., 75 (2007), pp. 205308/1205308/9.

M. Winkelnkemper, R. Seguin, S. Rodt, A. Schliwa, L. Reimann, A. Strittmatter, A. Hoffmann, D. Bimberg, Polarized emission lines from A and Btype excitonic complexes in single InGaN/GaN quantum dots, Journal of Applied Physics, 101 (2007), pp. 113708/1113708/4.

U. Wulf, P.N. Racec, E.R. Racec, Admittance of planar twoterminal quantum systems, Phys. Rev. B., 75 (2007), pp. 075320/1075320/9.

J. Elschner, H.Chr. Kaiser, J. Rehberg, G. Schmidt, $W^1,q$ regularity results for elliptic transmission problems on heterogeneous polyhedra, Mathematical Models & Methods in Applied Sciences, 17 (2007), pp. 593615.

H. Neidhardt, J. Rehberg, Scattering matrix, phase shift, spectral shift and trace formula for onedimensional Schrödingertype operators, Integral Equations and Operator Theory, 58 (2007), pp. 407431.
Abstract
The paper is devoted to Schroedinger operators on bounded intervals of the real axis with dissipative boundary conditions. In the framework of the LaxPhillips scattering theory the asymptotic behaviour of the phase shift is investigated in detail and its relation to the spectral shift is discussed, in particular, trace formula and BirmanKrein formula are verified directly. The results are used for dissipative SchroedingerPoisson systems. 
P.N. Racec, U. Wulf, Smallsignal circuit elements of MIStype nanostructures, Solid State Phenomena, 121123 (2007), pp. 549552.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Classical solutions of quasilinear parabolic systems on two dimensional domains, NoDEA. Nonlinear Differential Equations and Applications, 13 (2006), pp. 287310.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Convexity of trace functionals and Schrödinger operators, Journal of Functional Analysis, 234 (2006), pp. 4569.

M. Baro, N. Ben Abdallah, P. Degond, A. El Ayyadi, A 1D coupled Schrödinger driftdiffusion model including collisions, Journal of Computational Physics, 203 (2005), pp. 129153.

M. Baro, H. Neidhardt, J. Rehberg, Current coupling of driftdiffusion models and dissipative SchrödingerPoisson systems: Dissipative hybrid models, SIAM Journal on Mathematical Analysis, 37 (2005), pp. 941981.

TH. Koprucki, M. Baro, U. Bandelow, Th. Tien, F. Weik, J.W. Tomm, M. Grau, M.Ch. Amann, Electronic structure and optoelectronic properties of strained InAsSb/GaSb multiple quantum wells, Applied Physics Letters, 87 (2005), pp. 181911/1181911/3.

H. Neidhardt, J. Rehberg, Uniqueness for dissipative SchrödingerPoisson systems, Journal of Mathematical Physics, 46 (2005), pp. 113513/1113513/28.

M. Baro, H.Chr. Kaiser, H. Neidhardt, J. Rehberg, A quantum transmitting SchrödingerPoisson system, Reviews in Mathematical Physics. A Journal for Both Review and Original Research Papers in the Field of Mathematical Physics, 16 (2004), pp. 281330.

M. Baro, H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Dissipative SchrödingerPoisson systems, Journal of Mathematical Physics, 45 (2004), pp. 2143.

M. Baro, H. Neidhardt, Dissipative Schrödingertype operator as a model for generation and recombination, Journal of Mathematical Physics, 44 (2003), pp. 23732401.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Macroscopic current induced boundary conditions for Schrödingertype operators, Integral Equations and Operator Theory, 45 (2003), pp. 3963.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, On 1dimensional dissipative Schrödingertype operators, their dilations and eigenfunction expansions, Mathematische Nachrichten, 252 (2003), pp. 5169.

H.Chr. Kaiser, H. Neidhardt, J. Rehberg, Density and current of a dissipative Schrödinger operator, Journal of Mathematical Physics, 43 (2002), pp. 53255350.

P. Exner, H. Neidhardt, V.A. Zagrebnov, Potential approximation to $delta'$: An inverse Klauder phenomenon with normresolvent convergence, Communications in Mathematical Physics, 224 (2001), pp. 593612.

U. Bandelow, H.Chr. Kaiser, Th. Koprucki, J. Rehberg, Spectral properties of $k cdot p$ Schrödinger operators in one space dimension, Numerical Functional Analysis and Optimization. An International Journal, 21 (2000), pp. 379409.

V.M. Adamyan, H. Neidhardt, On the absolutely continuous subspace for nonselfadjoint operators, , 210 (2000), pp. 542.

H.Chr. Kaiser, J. Rehberg, About a stationary SchrödingerPoisson system with KohnSham potential in a bounded two or threedimensional domain, Nonlinear Analysis. Theory, Methods & Applications. An International Multidisciplinary Journal. Series A: Theory and Methods, 41 (2000), pp. 3372.
Contributions to Collected Editions

M. Kantner, A. Mielke, M. Mittnenzweig, N. Rotundo, Mathematical modeling of semiconductors: From quantum mechanics to devices, in: Topics in Applied Analysis and Optimisation, M. Hintermüller, J.F. Rodrigues, eds., CIM Series in Mathematical Sciences, Springer Nature Switzerland AG, Cham, 2019, pp. 269293, DOI 10.1007/9783030331160 .
Abstract
We discuss recent progress in the mathematical modeling of semiconductor devices. The central result of this paper is a combined quantumclassical model that selfconsistently couples van Roosbroeck's driftdiffusion system for classical charge transport with a Lindbladtype quantum master equation. The coupling is shown to obey fundamental principles of nonequilibrium thermodynamics. The appealing thermodynamic properties are shown to arise from the underlying mathematical structure of a damped Hamitlonian system, which is an isothermal version of socalled GENERIC systems. The evolution is governed by a Hamiltonian part and a gradient part involving a Poisson operator and an Onsager operator as geoemtric structures, respectively. Both parts are driven by the conjugate forces given in terms of the derivatives of a suitable free energy. 
M. Kantner, Hybrid modeling of quantum light emitting diodes: Selfconsistent coupling of driftdiffusion, SchrödingerPoisson, and quantum master equations, in: Proc. SPIE 10912, B. Witzigmann, M. Osiński, Y. Arakawa, eds., Physics and Simulation of Optoelectronic Devices XXVII, SPIE Digital Library, Bellingham, 2019, pp. 10912OU/110912OU/8, DOI 10.1117/12.2515209 .
Abstract
The devicescale simulation of electrically driven solid state quantum light emitters, such as singlephoton sources and nanolasers based on semiconductor quantum dots, requires a comprehensive modeling approach, that combines classical device physics with cavity quantum electrodynamics. In a previous work, we have selfconsistently coupled the semiclassical driftdiffusion system with a Markovian quantum master equation in Lindblad form to describe (i) the spatially resolved current injection into a quantum dot embedded within a semiconductor device and (ii) the fully quantum mechanical lightmatter interaction in the coupled quantum dotphoton system out of one box. In this paper, we extend our hybrid quantumclassical modeling approach by including a Schroedinger?Poisson problem to account for energy shifts of the quantum dot carriers in response to modifications of its macroscopic environment (e.g., quantum confined Stark effect due to the diode's internal electric field and plasma screening). The approach is demonstrated by simulations of a singlephoton emitting diode. 
M. Kantner, Simulation of quantum light sources using the selfconsistently coupled SchrödingerPoissonDriftDiffusionLindblad system, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2019, J. Piprek, K. Hinzer, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 1516, DOI 10.1109/NUSOD.2019.8806839 .
Abstract
The devicescale simulation of electrically drivenquantum light sources based on semiconductor quantum dotsrequires a combination of the (classical) semiconductor deviceequations with cavity quantum electrodynamics. In this paper, weextend our previously developed hybrid quantumclassical modelsystem ? where we have coupled the driftdiffusion system witha Lindbladtype quantum master equation ? by including a selfconsistent Schrödinger?Poisson problem. The latter describes the(quasi)bound states of the quantum dot carriers. The extendedmodel allows to describe the biasdependency of the emissionspectrum due to the quantum confined Stark effect 
TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, On a database of simulated TEM images for In(Ga)As/GaAs quantum dots with various shapes, in: Proceedings of the 19th International Conference on Numerical Simulation of Optoelectronic Devices  NUSOD 2019, J. Piprek, K. Hinze, eds., IEEE Conference Publications Management Group, Piscataway, 2019, pp. 1314, DOI 10.1109/NUSOD.2019.8807025 .

A. Maltsi, Th. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, Modelbased geometry reconstruction of quantum dots from TEM, in: 89th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), 18 of Proceedings in Applied Mathematics and Mechanics (PAMM), WileyVCH, Weinheim, 2018, pp. e201800398/1e201800398/2, DOI 10.1002/pamm.201800398 .

M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantumclassical modeling approach for electrically driven quantum dot devices, in: Proc. SPIE 10526, Physics and Simulation of Optoelectronic Devices XXVI, B. Witzigmann, M. Osiński, Y. Arakawa, eds., SPIE Digital Library, 2018, pp. 1052603/11052603/6, DOI 10.1117/12.2289185 .
Abstract
The design of electrically driven quantum light sources based on semiconductor quantum dots, such as singlephoton emitters and nanolasers, asks for modeling approaches combining classical device physics with cavity quantum electrodynamics. In particular, one has to connect the wellestablished fields of semiclassical semiconductor transport theory and the theory of open quantum systems. We present a first step in this direction by coupling the van Roosbroeck system with a Markovian quantum master equation in Lindblad form. The resulting hybrid quantumclassical system obeys the fundamental laws of nonequilibrium thermodynamics and provides a comprehensive description of quantum dot devices on multiple scales: It enables the calculation of quantum optical figures of merit (e.g. the second order intensity correlation function) together with the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. 
M. Kantner, M. Mittnenzweig, Th. Koprucki, Modeling and simulation of electrically driven quantum light sources: From classical device physics to open quantum systems, in: 14th International Conference on Nonlinear Optics and Excitation Kinetics in Semiconductors, September 2327, 2018, Berlin, Germany (Conference Program), 2018, pp. 135.

TH. Koprucki, A. Maltsi, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Towards modelbased geometry reconstruction of quantum dots from TEM, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 115116.

O. Marquardt, P. Mathé, Th. Koprucki, M. Caro, M. Willatzen, Datadriven electronic structure calculations in semiconductor nanostructures  beyond the eightband k.p formalism, in: Proceedings of the 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), A. Djurišić, J. Piprek, eds., IEEE Conference Publications Management Group, Piscataway, NJ, 2018, pp. 5556.

M. Kantner, U. Bandelow, Th. Koprucki, H.J. Wünsche, Multiscale modelling and simulation of singlephoton sources on a device level, in: EuroTMCS II  Theory, Modelling & Computational Methods for Semiconductors, 7th  9th December 2016, Tyndall National Institute, University College Cork, Ireland, E. O'Reilly, S. Schulz, S. Tomic, eds., Tyndall National Institute, 2016, pp. 65.

M. Kantner, U. Bandelow, Th. Koprucki, H.J. Wünsche, Modeling and numerical simulation of electrically pumped singlephoton emitters, in: Proceedings of the 15th International Conference on Numerical Simulation of Optoelectronic Devices 2015, J. Piprek, W. YuhRenn, eds., IEEE Conference Publications Management Group, Piscataway, 2015, pp. 151152.

D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, M. Virgilio, S. Guha, Th. Schröder, G. Capellini, Th. Koprucki, On device concepts for CMOScompatible edgeemitters based on strained germanium, in: Proceedings of the 15th International Conference on Numerical Simulation of Optoelectronic Devices 2015, J. Piprek, W. YuhRenn, eds., IEEE Conference Publications Management Group, Piscataway, 2015, pp. 129130.

G. Capellini, M. Virgilio, Y. Yamamoto, L. Zimmermann, B. Tillack, D. Peschka, M. Thomas, A. Glitzky, R. Nürnberg, K. Gärtner, Th. Koprucki, Th. Schroeder, Modeling of an edgeemitting strainedGe laser, in: Advanced Solid State Lasers, OSA Technical Digest (online) (Optical Society of America, 2015), 2015, pp. ATu2A.19/1ATu2A.19/3.
Abstract
By using fullycoupled 2D optoelectronic simulations with embedded microscopic gain calculations, we study the optoelectronic performance of a monolithically integrated edgeemitting laser based on strained germanium microstrips fabricated using CMOS standard processes. 
A. Mielke, On thermodynamical couplings of quantum mechanics and macroscopic systems, in: Mathematical Results in Quantum Mechanics. Proceedings of the QMath12 Conference, P. Exner, W. König, H. Neidhardt, eds., World Scientific Publishing, Singapore, 2015, pp. 331348.
Abstract
Pure quantum mechanics can be formulated as a Hamiltonian system in terms of the Liouville equation for the density matrix. Dissipative effects are modeled via coupling to a macroscopic system, where the coupling operators act via commutators. Following Öttinger (2010) we use the GENERIC framework to construct thermodynamically consistent evolution equations as a sum of a Hamiltonian and a gradientflow contribution, which satisfy a particular noninteraction condition:
We give three applications of the theory. First, we consider a finitedimensional quantum system that is coupled to a finite number of simple heat baths, each of which is described by a scalar temperature variable. Second, we model quantum system given by a onedimensional Schrödinger operator connected to a onedimensional heat equation on the left and on the right. Finally, we consider thermooptoelectronics, where the MaxwellBloch system of optics is coupled to the energydriftdiffusion system for semiconductor electronics. 
A. Glitzky, A. Mielke, L. Recke, M. Wolfrum, S. Yanchuk, D2  Mathematics for optoelectronic devices, in: MATHEON  Mathematics for Key Technologies, M. Grötschel, D. Hömberg, J. Sprekels, V. Mehrmann ET AL., eds., 1 of EMS Series in Industrial and Applied Mathematics, European Mathematical Society Publishing House, Zurich, 2014, pp. 243256.

P.N. Racec, R. Racec, H. Neidhardt, Rmatrix formalism for electron scattering in two dimensions with applications to nanostructures with quantum dots, in: Trends in Nanophysics, A. Aldea, V. Bârsan, eds., Engineering Materials, Springer, Berlin/Heidelberg, 2010, pp. 149174.
Abstract
We investigate the scattering phenomena in two dimensions produced by a general finiterange nonseparable potential. This situation can appear either in a Cartesian geometry or in a heterostructure with cylindrical symmetry. Increasing the dimensionality of the scattering problem new processes as the scattering between conducting channels and the scattering from conducting to evanescent channels are allowed. For certain values of the energy, called resonance energy, the transmission through the scattering region changes dramatically in comparison with an onedimensional problem. If the potential has an attractive character even the evanescent channels can be seen as dips of the total transmission. The multichannel current scattering matrix is determined using its representation in terms of the Rmatrix. The resonant transmission peaks are characterized quantitatively through the poles of the current scattering matrix. Detailed maps of the localization probability density sustain the physical interpretation of the resonances. Our formalism is applied to a quantum dot in a two dimensional electron gas and a conical quantum dot embedded inside a nanowire. 
J. Behrndt, M.M. Malamud, H. Neidhardt, Finite rank perturbations, scattering matrices and inverse problems, in: Operator Theory in Krein Spaces and Spectral Analysis, J. Behrndt, K.H. Förster, C. Trunk, H. Winkler, eds., 198 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2009, pp. 6185.
Abstract
In this paper the scattering matrix of a scattering system consisting of two selfadjoint operators with finite dimensional resolvent difference is expressed in terms of a matrix Nevanlinna function. The problem is embedded into an extension theoretic framework and the theory of boundary triplets and associated Weyl functions for (in general nondensely defined) symmetric operators is applied. The representation results are extended to dissipative scattering systems and an explicit solution of an inverse scattering problem for the LaxPhillips scattering matrix is presented. 
J. Behrndt, M. Malamud, H. Neidhardt, Trace formula for dissipative and coupled scattering systems, in: Spectral Theory in Inner Product Spaces and Applications, J. Behrndt, K.H. Förster, H. Langer, C. Trunk, eds., 188 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2008, pp. 5793.
Abstract
For scattering systems consisting of a (family of) maximal dissipative extension(s) and a selfadjoint extension of a symmetric operator with finite deficiency indices, the spectral shift function is expressed in terms of an abstract TitchmarshWeyl function and a variant of the BirmanKrein formula is proved. 
S. Ahmed, M. Usman, C. Heitzinger, R. Rahman, A. Schliwa, G. Klimeck, Symmetry breaking and fine structure splitting in zincblende quantum dots: Atomistic simulations of longrange strain and piezoelectric field, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 849850.

J. Behrndt, H. Neidhardt, J. Rehberg, Block matrices, optical potentials, trace class perturbations and scattering, in: Operator Theory in Inner Product Spaces, K.H. Förster, P. Jonas, H. Langer, C. Trunk, eds., 175 of Operator Theory: Advances and Applications, Birkhäuser, Basel, 2007, pp. 3349.

C. Cornet, M. Hayne, A. Schliwa, F. Doré, C. Labbé, H. Folliot, J. Even, D. Bimberg, Theory and experiment of InAs/InP quantum dots: From calculations to laser emission, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 779780.

F. Doré, C. Cornet, A. Schliwa, N. Bertru, O. Dehaese, I. Alghoraibi, H. Folliot, R. Piron, A. Le Corre, A theoretical and experimental study of $>2 mu$m luminescence of quantum dots on InP substrate, in: Physics of Semiconductors, W. Jantsch, F. Schäffler, eds., 893 of AIP Conference Proceedings, Springer, Berlin [et al.], 2007, pp. 889890.

U. Wulf, P.N. Racec, H. Richter, Quantentransport in Nanotransistoren, in: vol. 90 (2007) of Sitzungsberichte der LeibnizSozietät, traem fo verlag dr. wolfgang weist, Berlin, pp. 121137.

J. Behrndt, M.M. Malamud, H. Neidhardt, Scattering systems and characteristic functions, in: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2006), Kyoto, Japan, July 2428, 2006, pp. 19401945.

H.Chr. Kaiser, U. Bandelow, Th. Koprucki, J. Rehberg, Modelling and simulation of strained quantum wells in semiconductor lasers, in: Mathematics  Key Technology for the Future. Joint Projects Between Universities and Industry, W. Jäger, H.J. Krebs, eds., Springer, Berlin [u.a.], 2003, pp. 377390.

U. Bandelow, H. Gajewski, H.Chr. Kaiser, Modeling combined effects of carrier injection, photon dynamics and heating in Strained MultiQuantumWell Laser, in: Physics and Simulation of Optoelectronic Devices VIII, R.H. Binder, P. Blood, M. Osinski, eds., 3944 of Proceedings of SPIE, SPIE, Bellingham, WA, 2000, pp. 301310.

H.Chr. Kaiser, J. Rehberg, About some mathematical questions concerning the embedding of SchrödingerPoisson systems into the driftdiffusion model of semiconductor devices, in: EQUADIFF 99: International Conference on Differential Equations, Berlin 1999, B. Fiedler, K. Gröger, J. Sprekels, eds., 2, World Scientific, Singapore [u. a.], 2000, pp. 13281333.
Preprints, Reports, Technical Reports

O. Marquardt, Simulating the electronic properties of semiconductor nanostructures using multiband $kcdot p$ models, Preprint no. 2773, WIAS, Berlin, 2020, DOI 10.20347/WIAS.PREPRINT.2773 .
Abstract, PDF (706 kByte)
The eightband $kcdot p$ formalism been successfully applied to compute the electronic properties of a wide range of semiconductor nanostructures in the past and can be considered the backbone of modern semiconductor heterostructure modelling. However, emerging novel material systems and heterostructure fabrication techniques raise questions that cannot be answered using this wellestablished formalism, due to its intrinsic limitations. The present article reviews recent studies on the calculation of electronic properties of semiconductor nanostructures using a generalized multiband $kcdot p$ approach that allows both the application of the eightband model as well as more sophisticated approaches for novel material systems and heterostructures.
Talks, Poster

O. Marquardt, Datadriven electronic structure calculations for semiconductor nanostructures, Efficient algorithms for numerical problems  Workshop on the occasion of the retirement of Peter Mathé, January 17, 2020, WIAS Berlin, January 17, 2020.

O. Marquardt, Electronic properties of semiconductor heterostructures using SPHInX (online tutorial), NUSOD 2020: 20th International Conference on Numerical Simulation of Optoelectronic Devices (Online Event), September 14  25, 2020, Politecnico di Torino, September 14, 2020.

O. Marquardt, Nucleation chronology and electronic properties of In(As,Sb,P) gradedcomposition quantum dots (online talk), NUSOD 2020: 20th International Conference on Numerical Simulation of Optoelectronic Devices (Online Event), September 14  25, 2020, Politecnico di Torino, September 14, 2020.

O. Marquardt, Nucleation chronology and electronic properties of In(As,Sb,P) gradedcomposition quantum dots (online talk), CMD2020GEFES (Online Event), August 31  September 4, 2020, European Physical Society & La Real Sociedad Española de Física, September 4, 2020.

O. Marquardt, Th. Koprucki, A. Mielke, DESCANT  Datadriven electronic structure calculations for semiconductor nanostructures (online poster session), MATH+ Day 2020 (Online Event), November 6, 2020.

O. Marquardt, Semiconductor nanostructures (online talk), IKZWIAS Workshop (Online Event), October 30, 2020, WIAS Berlin, IKZ Berlin, October 30, 2020.

TH. Koprucki, K. Tabelow, T. Streckenbach, T. Niermann, A. Maltsi, Modelbased geometry reconstruction of TEM images (online poster session), MATH+ Day 2020 (Online Event), November 6, 2020.

A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Modelbased geometry reconstruction of quantum dots from TEM, Microscopy Conference 2019, Poster session IM 4, Berlin, September 1  5, 2019.

A. Maltsi, Th. Koprucki, T. Streckenbach, K. Tabelow, J. Polzehl, Modelbased geometry reconstruction of quantum dots from TEM, BMS Summer School 2019: Mathematics of Deep Learning, Berlin, August 19  30, 2019.

M. Kantner, Hybrid modeling of quantum light emitting diodes: Selfconsistent coupling of driftdiffusion, SchrödingerPoisson, and quantum master equations, SPIE Photonics West, February 5  7, 2019, San Francisco, USA, February 6, 2019, DOI 10.1117/12.2515209 .

M. Kantner, Simulation of quantum light sources using the selfconsistently coupled SchrödingerPoissonDriftDiffusionLindblad system, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD), July 8  12, 2019, University of Ottawa, Canada, July 8, 2019.

O. Marquardt, Charge confining mechanisms in IIIV semiconductor nanowires, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2019), July 8  12, 2019, University of Ottawa, Canada, July 8, 2019.

O. Marquardt, Datadriven electronic structure calculations for nanostructures (DESCANT), Sondierungsworkshop MPIE/WIAS ``Elektrochemie, Halbleiternanostrukturen und Metalle", October 14  15, 2019, MaxPlanckInstitut für Eisenforschung GmbH Düsseldorf, October 15, 2019.

O. Marquardt, Modelling the electronic properties of semiconductor nanowires, Engineering Physics Seminar, McMaster University, Hamilton, Canada, July 12, 2019.

TH. Koprucki, On a database of simulated TEM images for In(Ga)As/GaAs quantum dots with various shapes, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2019) , Session ``Nanostructures", July 8  12, 2019, University of Ottawa, Canada, July 8, 2019.

TH. Koprucki, Towards multiscale modeling of IIINbased LEDs, 19th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2019) , Session ``Postdeadline Session and Outlook", July 8  12, 2019, University of Ottawa, Canada, July 12, 2019.

A. Maltsi, Th. Koprucki, T. Niermann, T. Streckenbach, K. Tabelow, J. Polzehl, Computing TEM images of semiconductor nanostructures, Applied Mathematics and Simulation for Semiconductors (AMaSiS 2018), WIAS Berlin, October 8  10, 2018.

M. Kantner, M. Mittnenzweig, Th. Koprucki, A hybrid quantumclassical modeling approach for electrically driven quantum dot devices, SPIE Photonics West 2018: Physics and Simulation of Optoelectronic Devices XXVI, January 29  February 1, 2018, The Moscone Center, San Francisco, USA, January 29, 2018.

M. Kantner, Hybrid quantumclassical modeling of quantum dot based singlephoton emitting diodes, Workshop Applied Mathematics and Simulation for Semiconductors, WIAS Berlin, October 10, 2018.

M. Kantner, Modeling and simulation of electrically driven quantum light emitters, Leibniz MMS Days, Leibniz Institut für Oberflächenmodifizierung (IOM), Leipzig, March 2, 2018.

M. Kantner, Thermodynamically consistent modeling of electrically driven quantum dot based light emitters on a device scale, Workshop ,,Nonlinear Dynamics in Semiconductor Lasers (NDSL2018)'', June 18  20, 2018, WIAS, Berlin, June 18, 2018.

TH. Koprucki, Towards modelbased geometry reconstruction of quantum dots from TEM, 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018), Session ``Nanostructures'', November 5  9, 2018, The University of Hong Kong, China, November 8, 2018.

O. Marquardt, Computational design of coreshell nanowire crystalphase quantum rings for the observation of AharonovBohm oscillations, 18th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD 2018) , Session " Nanostructures", November 5  9, 2018, The University of Hong Kong, China, November 6, 2018.

M. Kantner, Hybrid quantumclassical modeling of electrically driven quantum light sources, Meeting of the MATHEON Scientific Advisory Board 2017, TU Berlin, Institut für Mathematik, November 13, 2017.

M. Kantner, Simulations of quantum dot devices by coupling of quantum master equations and semiclassical transport theory, 17th International Conference on Numerical Simulation of Optoelectronic Devices (NUSOD2017), July 24  28, 2017, Technical University of Denmark, Copenhagen, July 27, 2017.

A. Mielke, Mathematical modeling of semiconductors: From quantum mechanics to devices, CIMWIAS Workshop ``Topics in Applied Analysis and Optimisation'', December 6  8, 2017, Centro de Matemática, Lisboa, Portugal, December 8, 2017.

M. Mittnenzweig, Gradient flow structures for quantum master equations, AnalysisSeminar AugsburgMünchen, Universität Augsburg, Institut für Mathematik, June 8, 2017.

M. Kantner, Multiscale modeling and numerical simulation of singlephoton emitters, Matheon Workshop9th Annual Meeting ``Photonic Devices", Zuse Institut, Berlin, March 3, 2016.

M. Kantner, Multiscale modelling and simulation of singlephoton sources on a device level, EuroTMCS II Theory, Modelling & Computational Methods for Semiconductors, Tyndall National Institute and University College Cork, Cork, Ireland, December 9, 2016.

A. Mielke, On entropic gradient structures for classical and quantum Markov processes with detailed balance, Pure Analysis and PDEs Seminar, Imperial College London, Department of Mathematics, UK, May 11, 2016.

M. Kantner, Multiscale modeling and simulation of electrically pumped singlephoton sources, International NanoOptoelectronics Workshop (iNOW 2015), Tokio, Japan, August 3  7, 2015.

A. Mielke, Geometric approaches at and for theoretical and applied mechanics, Phil Holmes Retirement Celebration, October 8  9, 2015, Princeton University, Mechanical and Aerospace Engineering, New York, USA, October 8, 2015.

P.N. Racec, Transport in semiconductor nanowires with constrictions: Cylindrical quantum point contact, 3èmes Journées Modélisation et Calcul, March 21  22, 2013, Université de Reims ChampagneArdenne, Laboratoire de Mathématiques, France, March 21, 2013.

P.N. Racec, WignerEisenbud problem within finite volume method: application to electronic transport in cylindrical nanowire heterostructures, QMATH12  Mathematical Results in Quantum Mechanics, September 10  13, 2013, HumboldtUniversität zu Berlin, Berlin, September 12, 2013.

A. Mielke, Coupling quantum mechanical systems with dissipative environments via GENERIC, Applied Analysis Seminar, University of Bath, Department of Mathematical Sciences, UK, May 23, 2013.

A. Mielke, Entropydriven dissipative coupling of quantum mechanics to simple heat baths, QMATH12  Mathematical Results in Quantum Mechanics, September 10  13, 2013, HumboldtUniversität zu Berlin, Berlin, September 10, 2013.

A. Mielke, Mathematische und thermodynamische Modellierung von Halbleiterstrukturen, BlockSeminar des SFB 787 ``Nanophotonik'', May 6  8, 2013, Technische Universität Berlin, GraalMüritz, May 8, 2013.

A. Mielke, On entropydriven dissipative quantum mechanical systems, Analysis and Stochastics in Complex Physical Systems, March 20  22, 2013, Universität Leipzig, Mathematisches Institut, March 21, 2013.

A. Mielke, Thermodynamic modeling of the MaxwellBloch and the semiconductor equations via GENERIC, Modeling, Analysis and Simulation of Optical Modes in Photonic Devices (MASOMO 13), April 10  12, 2013, WIAS Berlin, April 10, 2013.

H. Neidhardt, Boundary triplets and tunnel junction formula with applications, Mathematical Challenge of Quantum Transport in Nanosystems, March 12  15, 2013, Saint Petersburg National Research University of Informational Technologies, Mechanics, and Optics, Russian Federation, March 14, 2013.

P.N. Racec, Quantum modeling for semiconductor nanowires with embedded subsystems, Interdisciplinary Workshop on Quantum Device  through Mathematical Structure  2013, National Institute of Informatics/Okayama University, Tokyo, Japan, January 15, 2013.

A. Mielke, Dissipative quantum mechanics: Geometry meets thermodynamics, Symposium ``Recent Trends in Dynamical Systems'', dedicated to Jürgen Scheurle's 60th birthday, January 11  14, 2012, Technische Universität München, Zentrum Mathematik, January 11, 2012.

A. Mielke, On consistent couplings of quantum mechanical and dissipative systems, Jahrestagung der Deutschen MathematikerVereinigung (DMV) 2012, Minisymposium ``Dynamical Systems'', September 17  20, 2012, Universität des Saarlandes, Fakultät für Mathematik und Informatik, Saarbrücken, September 19, 2012.

H. Neidhardt, An application of the LandauerBüttiker formula to photon emitting and absorbing systems, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24  28, 2012, WIAS Berlin, September 28, 2012.

H. Neidhardt, JaynesCummings model coupled to leads: A model for LEDs?, Quantum Circle Seminar, Czech Technical University, Faculty of Nuclear Sciences and Physical Engineering, Doppler Institute for Mathematical Physics and Applied Mathematics, Prague, Czech Republic, March 13, 2012.

H. Neidhardt, LandauerBüttiker formula applied to photon emitting and absorbing systems, Kolloquium ``Mathematische Physik'', December 13  14, 2012, Technische Universität Clausthal/Technische Universität Braunschweig, ClausthalZellerfeld, December 14, 2012.

P.N. Racec, H. Neidhardt, H.Chr. Kaiser, R. Racec, Electronic quantum transport in semiconductor nanostructures, Fachtagung LeibnizNano (1. NanotechnologieWorkshop der LeibnizGemeinschaft), Berlin, January 30  31, 2012.

P.N. Racec, Fano regime of transport through open quantum dots, Seminar ``Quanteneffekte in Festkörpern'', Leibniz Universität Hannover, Institut für Festkörperphysik, June 13, 2012.

P.N. Racec, Finite volume discretization and Rmatrix formalism for cylindrical nanowire heterostructures, Seminar Laboratory 30 ``Nanoscale Condensed Matter Laboratory'', National Institute of Materials Physics, Bucharest, Romania, October 9, 2012.

P.N. Racec, Optimal finite volume discretization of Schrödinger equations for cylindrical symmetric nanowires, 76. Jahrestagung der DPG und DPG Frühjahrstagung 2012 of the Condensed Matter Section, Sektion ``Semiconductor Physics Division'', Sitzung ``Quanum Dots and Wires: Transport Properties I'', March 26  29, 2012, Technische Universität Berlin, March 28, 2012.

P.N. Racec, Quantum transport and the Rmatrix formalism for cylindrical nanowire heterostructures, Technische Universität Graz, Institut für Theoretische Physik, Austria, September 13, 2012.

P.N. Racec, Quantum transport in cylindrical nanowires with constrictions, 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), MiniSymposium ``Scattering problems for quantum, electromagnetic, and acoustic waveguides'', September 10  14, 2012, Universität Wien, Austria, September 10, 2012.

P.N. Racec, Quantum transport in semiconductor nanoheterostructures, International Workshop ``Mathematics for Semiconductur Heterostructures: Modeling, Analysis, and Numerics'', September 24  28, 2012, WIAS Berlin, September 28, 2012.

TH. Koprucki, Semiclassical modeling of quantum dot lasers with microscopic treatment of Coulomb scattering, Mathematical Challenges of Quantum Transport in NanoOptoelectronic Systems, February 4  5, 2011, WIAS, February 4, 2011.

A. Mielke, Geometry and thermodynamics for the coupling of quantum mechanics and dissipative systems, Workshop ``Applied Dynamics and Geometric Mechanics'', August 15  19, 2011, Mathematisches Forschungsinstitut Oberwolfach, August 16, 2011.

P.N. Racec, Efficient simulation of cylindrical nanowire heterostructures by means of the Rmatrix formalism, 75. Jahrestagung der DPG und DPG Frühjahrstagung 2011, Sektion ``Semiconductor Physics Division'', Sitzung ``Quantum Wires: Transport'', March 15  17, 2011, Technische Universität Dresden, March 16, 2011.

L. Wilhelm, An abstract LandauerBüttiker formula with application to a toy model of a quantum dot LED, Analysis Seminar, Aalborg University, Department of Mathematical Sciences, Denmark, June 16, 2011.

L. Wilhelm, An abstract approach to the LandauerBüttiker formula with application to an LED toy model, Mathematical Challenges of Quantum Transport in NanoOptoelectronic Systems, February 4  5, 2011, WIAS, February 5, 2011.

H. Neidhardt, Comments on the LandauerBüttiker formula and its applications, Quantum Transport Days, November 14  15, 2011, Université AixMarseille 2, Centre de Physique Théorique, France, November 14, 2011.

H. Neidhardt, Scattering for selfadjoint extensions, Analysis Seminar, Aalborg University, Department of Mathematical Sciences, Denmark, April 22, 2010.

H. Neidhardt, Scattering matrices and Weyl function, Research seminar of the Graduate School of Natural Science and Technology, Okayama University, Department of Mathematics, Japan, September 14, 2010.

P.N. Racec, Fano regime of transport through open quantum dots, International Workshop ``Advanced Functionality with ThreeDimensionally Controlled Quantum Structures'' within the Strategic JapaneseGerman Cooperative Program on ``Nanoelectronics'', August 30  31, 2010, PaulDrudeInstitut für Festkörperelektronik Berlin, Abteilung ``Semiconductor Spectroscopy'', Potsdam, August 31, 2010.

K. Hoke, Hartree solution of the KohnSham system for semiconductor devices, BerlinLeipzig Seminar on Numerics, MaxPlanckInstitut für Mathematik in den Naturwissenschaften, Leipzig, March 18, 2009.

K. Hoke, Iterative solution of the KohnSham system for semiconductor devices, International Conference ``Mathematics of Finite Elements and Applications 2009 (MAFELAP)'', Minisymposium ``Numerical Problems in Density Functional Theory'', June 9  12, 2009, The Brunel Institute of Computational Mathematics (BICOM), Uxbridge, UK, June 12, 2009.

TH. Koprucki, Spectral properties and band gap estimates for kp Hamiltonians for quantum wells, International NanoOptoelectronics Workshop (iNOW 2009), Stockholm, Sweden, and Berlin, Germany, August 2  15, 2009.

P.N. Racec, Evanescent channels and scattering in cylindrical nanowire heterostructures, Spring Meeting of the Deutsche Physikalische Gesellschaft, Session of Semiconductor Physics Division on Quantum Wires: Optical and Transport Properties, Deutsche Physikalische Gesellschaft/Technische Universität Dresden, March 24, 2009.

P.N. Racec, Evanescent channels and scattering in cylindrical nanowire heterostructures, Physikalisches Kolloquium, Brandenburgische Technische Universität Cottbus, April 14, 2009.

P.N. Racec, Quantum transport in cylindrical nanowire heterostructures: The scattering problem, PaulDrudeInstitut für Festkörperelektronik, Abteilung Epitaxie, Berlin, May 13, 2009.

H.Chr. Kaiser, Transient KohnSham theory, Jubiläumssymposium ``Licht  Materialien  Modelle'' (100 Jahre Innovation aus Adlershof), BerlinAdlershof, September 7  8, 2009.

H. Neidhardt, On carrier transport modeling in semiconductor devices at WIAS: A survey, Satellite Meeting of the International Congress of Mathematical Physics ``Mathematical Aspects of Quantum Transport and Applications in Nanophysics'', August 10  13, 2009, Aalborg University, Department of Mathematical Sciences, Denmark, August 10, 2009.

P.N. Racec, Scattering in cylindrical heterostructures, Workshop ``Trends in Nanoscience: Theory, Experiments, Technology'', August 23  30, 2009, Abdus Salam International Centre for Theoretical Physics, Trieste (ICTP), Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest (IFINHH), International Atomic Energy Agency, Vienna (IAEN), Sibiu, Romania, August 26, 2009.

P.N. Racec, Scattering states in cylindrical nanowire heterostructures, International NanoOptoelectronic Workshop (iNOW 2009), Stockholm, Sweden, and Berlin, Germany, August 2  15, 2009.

P.N. Racec, Scattering theory in cylindrical nanowire heterostructures, Seminar of Nonequilibrium ManyBody Systems Group, MartinLutherUniversität HalleWittenberg, Institut für Physik, December 7, 2009.

J. Rehberg, Functional analytic properties of the quantum mechanical particle density operator, International Workshop on Quantum Systems and Semiconductor Devices: Analysis, Simulations, Applications, April 20  24, 2009, Peking University, School of Mathematical Sciences, Beijing, China, April 21, 2009.

K. Hoke, Numerical treatment of the KohnSham system for semiconductor devices, Workshop on Mathematical Aspects of Transport in Mesoscopic Systems, Dublin, Ireland, December 4  7, 2008.

K. Hoke, On the numerics of the 3D KohnSham system, 4th Workshop on Mathematical Models for Transport in Macroscopic and Mesoscopic Systems, February 8  9, 2008, WIAS, February 9, 2008.

P.N. Racec, Electrical transport through quantum systems with nonseparable scattering potential, University of Iceland, Science Institute, Reykjavik, June 20, 2008.

H.Chr. Kaiser, A driftdiffusion model for semiconductors with internal interfaces, Annual Meeting of the Deutsche MathematikerVereinigung 2008, Minisymposium ``Analysis of ReactionDiffusion Systems with Internal Interfaces'', September 15  19, 2008, FriedrichAlexanderUniversität ErlangenNürnberg, September 15, 2008.

H.Chr. Kaiser, A thermodynamic approach to transient KohnSham theory, 100th Statistical Mechanics Conference, December 13  18, 2008, Rutgers, The State University of New Jersey, New Brunswick, USA, December 16, 2008.

H.Chr. Kaiser, On driftdiffusion KohnSham theory, 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM 2008), session ``Applied Analysis'', March 31  April 4, 2008, University of Bremen, April 1, 2008.

H. Neidhardt, KohnSham systems at zero temperature, Workshop on Mathematical Aspects of Transport in Mesoscopic Systems, December 4  7, 2008, Dublin Institute for Advanced Studies, School of Theoretical Physics, Ireland, December 5, 2008.

P.N. Racec, Quantum transport in cylindrical nanowire heterostructures, Workshop on Mathematical Aspects of Transport in Mesoscopic Systems, December 4  7, 2008, Dublin Institute for Advanced Studies, School of Theoretical Physics, Ireland, December 6, 2008.

K. Hoke, The KohnSham system in case of zero temperature, MiniWorkshop on PDE's and Quantum Transport, March 12  16, 2007, Aalborg University, Department of Mathematical Sciences, Denmark, March 15, 2007.

H.Chr. Kaiser, A driftdiffusion model of transient KohnSham theory, First Joint International Meeting between the American Mathematical Society and the Polish Mathematical Society, Special Session ``Mathematics of Large Quantum Systems'', July 31  August 3, 2007, University of Warsaw, Poland, August 3, 2007.

H. Neidhardt, On a quantum transmitting SchrödingerPoisson system, MiniWorkshop on PDE's and Quantum Transport, March 12  16, 2007, Aalborg University, Department of Mathematical Sciences, Denmark, March 15, 2007.

J. Rehberg, On SchrödingerPoisson systems, International Conference ``Nonlinear Partial Differential Equations'' (NPDE 2007), September 10  15, 2007, Institute of Applied Mathematics and Mechanics of NASU, Yalta, Ukraine, September 13, 2007.

J. Rehberg, Operator functions inherit monotonicity, MiniWorkshop on PDE's and Quantum Transport, March 12  16, 2007, Aalborg University, Department of Mathematical Sciences, Denmark, March 14, 2007.

J. Rehberg, Über SchrödingerPoissonSysteme, Chemnitzer Mathematisches Colloquium, Technische Universität Chemnitz, Fakultät für Mathematik, May 24, 2007.

J. Rehberg, The SchrödingerPoisson system, Colloquium in Honor of Prof. Demuth, September 10  11, 2006, Universität Clausthal, September 10, 2006.

H. Neidhardt, A quantum transmitting SchrödingerPoisson system, Workshop ``Quantum Transport and Exitations from Macro to Nanoscale: Theory and Applications'', November 10  13, 2005, Aalborg University, Denmark, November 11, 2005.

H. Neidhardt, Dissipative SchrödingerPoisson systems and uniqueness, Workshop on ``Mathematical Models of Nanostructures: Spectral Problems and Scattering Properties'', April 25  27, 2005, HumboldtUniversität zu Berlin, April 26, 2005.

H. Neidhardt, Hybrid models for semiconductors, Physikalisches Kolloquium, Brandenburgische Technische Universität Cottbus, Lehrstuhl für Theoretische Physik, November 29, 2005.

H.Chr. Kaiser, About quantum transmission on an up to three dimensional spatial domain, University of Texas at Dallas, USA, October 28, 2005.

H.Chr. Kaiser, An open quantum system driven by an external flow, Workshop ``Nonlinear spectral problems in solid state physics'', April 4  8, 2005, Institut Henri Poincaré, Paris, France, April 7, 2005.

H.Chr. Kaiser, Modeling and quasi3D simulation of indium grains in (In,Ga)N/GaN quantum wells by means of density functional theory, Physikalisches Kolloquium, Brandenburgische Technische Universität, Lehrstuhl Theoretische Physik, Cottbus, February 15, 2005.

H.Chr. Kaiser, On quantum transmission, Mathematical Physics Seminar, November 9  11, 2005, University of Texas at Austin, USA, November 9, 2005.

H.Chr. Kaiser, Quasi3D simulation of multiexcitons by means of density functional theory, Oberseminar ``Numerik/Wissenschaftliches Rechnen'', MaxPlanckInstitut für Mathematik in den Naturwissenschaften, Leipzig, January 11, 2005.

H.Chr. Kaiser, Spectral resolution of a velocity field on the boundary of a Lipschitz domain, 2nd Joint Meeting of AMS, DMV, ÖMG, June 16  19, 2005, Johannes GutenbergUniversität, Mainz, June 16, 2005.

J. Rehberg, Some analytical ideas concerning the quantumdriftdiffusion systems, Workshop ``Problèmes spectraux nonlinéaires et modèles de champs moyens'', April 4  8, 2005, Institut Henri Poincaré, Paris, France, April 5, 2005.

J. Rehberg, Analysis of macroscopic and quantum mechanical semiconductor models, International Visitor Program ``Nonlinear Parabolic Problems'', August 8  November 18, 2005, Finnish Mathematical Society (FMS), University of Helsinki, and Helsinki University of Technology, Finland, November 1, 2005.

H. Neidhardt, A model for resonant tunneling diodes, Seminar in Statistical Physics & Condensed Matter, July 2, 2004, Centre de Physique Théorique, Marseille, France, June 2, 2004.

H. Neidhardt, Hybrid models for semiconductors and dissipative SchrödingerPoisson systems, Academy of Sciences of the Czech Republic, Nuclear Physics Institute, Prague, February 17, 2004.

J. Fuhrmann, H.Chr. Kaiser, Th. Koprucki, G. Schmidt, Electronic states in semiconductor nanostructures and upscaling to semiclassical models, Evaluation Colloquium of the DFG Priority Program ``Analysis, Modeling and Simulation of Multiscale Problems'', Bad Honnef, May 20  21, 2004.

H. Gajewski, R. Hünlich, H.Chr. Kaiser, M. Baro, Quantum mechanical and macroscopic models for optoelectronic devices, DFG Research Center sc Matheon, Technische Universität Berlin, July 19, 2004.

H.Chr. Kaiser, Density functional theory for multiexcitons in quantum boxes, ``Molecular Simulation: Algorithmic and Mathematical Aspects'', Institut Henri Poincaré, Paris, France, December 1  3, 2004.

M. Baro, H. Gajewski, R. Hünlich, H.Chr. Kaiser, Optoelektronische Bauelemente: mikroskopische & makroskopische Modelle, MathInside  Überall ist Mathematik, event of the DFG Research Center ``Mathematics for Key Technologies'' on the occasion of the Open Day of Urania, Berlin, September 13, 2003  December 3, 2004.
Contact
Contributing Groups of WIAS
Mathematical Context
 Analysis of Partial Differential Equations and Evolutionary Equations
 Direct and inverse problems for the Maxwell equations
 Functional analysis and operator theory
 Multi scale modeling and hybrid models
 Multiscale Modeling and Asymptotic Analysis
 Systems of partial differential equations: modeling, numerical analysis and simulation
 Variational methods