Research Group "Partial Differential Equations"
Semiconductor Seminar
Organizer:
Prof. Dr. A. Mielke
Place/Time: WIAS, Karl Weierstrass lecture room (4th floor), Wednesdays, 10 a.m.
Contact: Dr. H. Neidhardt
26.02.2013 Attention: talk is at 10:00 a.m.
Florian Platzek (WIAS Berlin, Germany)
Basic Comments on the Maxwell-Bloch System
Abstract is here.
26.02.2013 Attention: talk is at 11:00 a.m.
Dr. Paul Racec (WIAS Berlin, Germany)
Transport in nanowires with constrictions: cylindrical quantum point contact
I will summarize the physical interpretation of the seminal experiments regarding the quantized linear conductance in a quantum point contact in the two-dimensional electron gas (2DEG) [B. J. van Wees et al., Phys. Rev. Lett. 60, 848 (1988) and D. A. Wharam et al., J. Phys. C 21, L209, (1988)]. The quantization of the conductance is not restricted only for constrictions in 2DEG and it appears also for constrictions in a three-dimensional electron gas (3DEG). One difference to the case of 2DEG is that the sequence of the conductance steps depends on the geometry of the nanowire cross-section through the degeneracy of the transversal modes. I will present our recent results on the transmission coefficient for a cylindrical semiconductor nanowire with one and two constrictions and their physical interpretation in terms of a cylindrical quantum point contact. The system with two constrictions offers a possibility for an experimental evidence of quasi-bound states of evanescent channels.
18.01.2013 Attention: talk is on Friday, 10:00 a.m. in Erhard-Schmidt-Hörsaal
Claus Köstler (University Colleg Cork, Irland)
Symmetrien in der nichtkommutativen WahrscheinlichkeitstheorieDie systematische Algebraisierung von Wahrscheinlichkeitstheorie führt zu deren nichtkommutativen Erweiterung, wie sie für die Beschreibung zufälliger Quantenereignisse hilfreich ist. Damit stellt sich auch die Frage, inwiefern sich fundamentale Ergebnisse zu distributionellen Symmetrien 'quantisieren' lassen. Beispielsweise besagt der Satz von de Finetti, dass eine unendliche Folge von austauschbaren Zufallsvariablen bedingt stochastisch unabhängig ist. Zufallsvariablen heissen hier austauschbar, wenn ihre gemeinsame Verteilung unter Permutationen der Zufallsvariablen invariant ist. Ich werde eine nichtkommutative Version dieses Satzes [1] vorstellen und darüber hinaus auf seine Rolle in der freien Wahrscheinlichkeitstheorie [2], der Theorie der Unterfaktoren [3] sowie der Darstellungstheorie der unendlichen symmetrischen Gruppe [4] eingehen.
Literatur:
[1] Köstler, Claus: A noncommutative extended de Finetti theorem. J. Funct. Anal. 258 (2010), no. 4, 1073 - 1120.
[2] Köstler, Claus; Speicher, Roland. A noncommutative de Finetti theorem: invariance under quantum permutations is equivalent to freeness with amalgamation. Comm. Math. Phys. 291 (2009), no. 2, 473 - 490.
[3] Gohm, Rolf; Köstler, Claus: Noncommutative independence from the braid group B∞. Comm. Math. Phys. 289 (2009), no. 2, 435 - 482.
[4 ]Gohm, Rolf; Köstler, Claus: Noncommutative independence from characters of the infinite symmetric group S∞. arXiv:1005.5726, 47 pages.
16.01.2013
Vladimir Lotoreichik (Graz University of Technology, Austria)
Self-adjoint Laplacians on partitions of Euclidean spaces with δ and δ'-couplingsIn the talk I will discuss self-adjoint Laplace operators on partitions of Euclidean spaces into finite number of bounded and unbounded Lipschitz domains. The problem becomes interesting when we pose local boundary conditions which connect neighboring domains in the partition. Spectral properties of the corresponding self-adjoint Laplacians turn out to be related to dierent combinatorial properties of the partition such as the number of colors sufficient to color all the domains in a way that neighboring domains have distinct colors or some path lengths in the corresponding graph of neighborhoods. This talk is based on the joint work with Jussi Behrndt and Pavel Exner.
09.01.2013 Attention: this talk is canceled
Florian Platzek (WIAS Berlin, Germany)
Basic Comments on the Maxwell-Bloch SystemThe interaction of matter and light can be described by the Maxwell- Bloch system. The system couples the classical Maxwell equations for the electro magnetic field (E;H) for light with a quantum mechanical equation for the matter, which is described by the density matrix ρ. The main focus of this talk lies on the presentation of existence and uniqueness results for the semilinear symmetric hyperbolic system
∂/∂t E - curl H = -∂/∂t P
∂/∂t H + curl E = 0
i∂/∂t ρ = [Ω - ΓE,ρ]
where the coupling is given via P = Tr(Γρ). Following closely the lines of [JMR2000], one is lead to a special case of the results from [Dumas2005], where both a more general right hand side and a more general coupling are considered. Besides this, some general comments on the structure of the system, the conserved quantities and the physical background are made.
[JMR2000] J.L. Joly & G. Metivier & J. Rauch, Global Solutions to Maxwell Equations in a Ferromagnetic Medium, Ann. Henri Poincare (2000) p. 307-340, Birkhaeuser Verlag, Basel.
[Dumas2005] E. Dumas, Global Existence for Maxwell-Bloch Systems, J. Diff. Eq. 219 (2005) p. 484-509.
28.11.2012
Dr. L. I. Goray (Saint Petersburg Academic University, Russia)
Energy state calculus in complex structures comprising quantum dotsElectro- and photo-luminescence of quantum dot (QD) based opto-electronic devices are connected with electron transitions between the electron and hole levels of QDs. The main peaks in the spectra of a single QD or a QD ensemble are connected with electron transitions between ground and excited QD states. QDs have parameters superior to quantum well (QW) analogues because of a long electron lifetime in excited states, but combinations of both low-dimensional quantum structures may have additional advantages. The author considers various geometries of semiconductor devices and different quantum-mechanical models applied to their electronic structure study. This plays the predominate role to solve the Schrödinger equation and to find electron and hole wave functions and energy states. Three well-known numerical ways to find energy levels of such complex structures, namely the effective mass approach, the close-coupling method, and the pseudopotential method can be used. Some advantages and disadvantages of these approaches vs. shapes and sizes of QDs are emphasized. It has been shown the most universal and powerful method of pseudopotential can be applied to the electronic state analysis of the complex 3D InGaAs/GaAs structure combined a QW, a nanobridge, and a QD with different material parameters, band offsets and effective masses.
07.11.2012
J. M. Castelo (Hochschule RheinMain, Rüsselsheim)
Numerical analysis of few-electron transport in multi-gate nanowire field-effect transistors: A multi-configurational approachWe consider a nanowire-based field-effect transistor (NWFET) with a coaxial gate geometry. For the theoretical description of one-dimensional (1D) non-equilibrium transport, we employ a Green's function formalism (NEGF). Few-electron Coulomb charging effects due to resonantly trapped electrons are taken into account by use of a multi-configurational approach (MCSCG). The electrostatics within the channel and the Coulomb interaction between electrons are described by a Coulomb Green's function. Based on these concepts, the open source simulation tool "NWFET-Lab" was developed. We use this simulation tool for the study of electronic transport in a multi-gate NWFET. Using multiple bias and control gate electrodes, the channel's axial potential profile can be defined. We analyze the influence of the position and length of the control gate segment on the electronic transport characteristics.
24.10.2012
Dr. Valeriu Moldoveanu (NIMP Bucharest, Romania)
On the steady-state regime of open interacting systemsWe address the transport problem in interacting mesoscopic systems for two relevant physical situations:
i) the so-called partitioning approach in which the finite mesoscopic sample is coupled to non-interacting b iased leads at some intial instant t0 and
ii) the partition-free setup where the initially coupled sample is submitted to a bias at t0.
In both scenarios we prove the existence of a steady-state regime both for current and correlation Green functions.
For the partitioned setting we show that they depend neither on the initial state of the sample nor on the switching profile. Closed formulae for the steady-state current are also derived. In the partitioning approach the 1st order correction w.r.t the interaction strength contains the mean-field (Hartree-Fock) results and leads to the Landauer formula.
The starting point of our analysis is the 'lesser' correlation function one uses in the Keldysh formalism. However, rather than developing the perturbation theory for contour-ordered Greens' functions we use the time-dependent scattering theory and the Wick theorem. While the approach is perturbative with regard to the interaction strength, the existence of the stationary regime is general in the sense that it does not rely on a particular approximation scheme for the Coulomb effects.
27.06.2012 Attention: this talk takes place in Erhard Schmidt lecture room and starts at 1.30 p.m.
Kaczmarkiewicz, Piotr (Wilhelms-Universität Münster, Institut für Festkörpertheorie)
Non-uniformly shaped quantum dashes: Electronic and optical properties
16.05.2012 Attention: this talk takes place in Erhard Schmidt lecture room and starts at 1.30 p.m.
Dr. Valeriu Moldoveanu (NIMP Bucharest, Romania)
Off-resonant transport in interacting quantum dotsAbstract:
Consider a bunch of interacting electrons confined in a quantum dot (QD) which is suddenly coupled to semi-infinite and non-interacting biased leads at an initial instant t = 0. We study the 'off-resonant' regime which means that the discrete spectrum of the isolated sample is located far away from the absolutely continuous spectrum of the leads. In this case the existence of a stationary regime is presumably prohibited due to the oscillations coming from bound states. Therefore we focused on the perturbative expansion of the ergodic current w.r. to the lead-dot coupling parameter τ. We explicitely calculate the second and fourth order contributions which physically correspond to the sequential and cotunneling processes and find some physically meaningful features: a) In the interacting case the ergodic cotunneling current depends on the initial many-body configuration of the isolated QD. b) In the non-interacting case the ergodic current is given by the first term in the expansion w.r.t τ of the famous Landauer formula. c) Our explicit formula for the transient sequential current exhibits long-time oscillations that are qualitively reproduced by the generalized master equation (GME) method.
The talk is based on the paper 'On the cotunneling regime of interacting quantum dots' (J. Phys. A: Math. Theor. 44, 305002 (2011)) written in collaboration with H. D. Cornean (IMF Aalborg).
02.05.2012 Attention: this talk takes place in Erhard Schmidt lecture room and starts at 11 a.m.
Prof. Dr. Jussi Behrndt (TU Graz, Austria)
Spectral theory of Schrödinger operators with delta-potentialsAbstract:
In this talk we study spectral properties of selfadjoint Schrödinger operators with δ and δ'-potentials supported on a smooth compact hypersurface. Furthermore, Schatten-von Neumann type estimates for the differences of the powers of the resolvents of the Schrödinger operators with δ and δ'-potentials, and the Schrödinger operator without a singular interaction are discussed.
21.03.2012
Dr. Boris Schäfer-Bung (FU Berlin)
Dimension reduction by balanced truncation: Application to light-induced control of classical dynamics and open quantum systemsAbstract:
In this talk, the balanced truncation is introduced as a powerful technique to reduce the state-space dimension of a system. Its basic principle is to identify a subspace of jointly easily controllable and observable states and then to restrict the dynamics to this subspace without changing the overall response of the system. The method is applied to a model system in classical dynamics and to an open quantum model system. Both describe the dynamics of a particle in a double well potential driven by an external control field. The accuracy of dimension reduction is investigated by comparing the dynamics obtained for the truncated system versus those for the original system.
07.03.2012
Dr. Caspar Leendertz (Helmholtz-Zentrum Berlin für Materialien und Energie)
Effizienzlimitierende Rekombinationsprozesse in amorph/kristallinen und polykristallinen Siliziumsolarzellen
01.12.2011 Attention: this talk takes place on Thursday and starts at 11 a.m.
Prof. Dr. Gernot Paasch (IWF Dresden)
Gaussian transport states in organic devices
07.09.2011
Prof. Dr. Alexander Mielke (WIAS Berlin)
Global existence and convergence to thermal equilibrium in a class of dissipative quantum systems
02.03.2011
Prof. Dr. Wataru Izuminda (Tohoku University, Sendai, Japan)
Curvature effects in rolled-up semiconductor layers and carbon nanotubesAbstract:
Two topics concerning the curvature effects in our recent study will be presented.
First talk is about vibrational properties of free-standing rolled-up semiconductor layers. Recently, the eigenfrequency of the rolled-up semiconductor layer systems has been experimentally observed. Motivated by the measurement, we theoretically study the vibration of rolled-up semiconductor layers. When the curvature increases, the frequencies for the axially waving modes become higher, whereas the frequencies for the fundamental bending and twisting modes keeping almost constant. The curvature dependence can be explained with an analytical expression.
Second talk is about a spin-orbit interaction in single wall carbon nanotubes. Spin properties on the carbon nanotubes have been investigated as well as their charge conductor properties. Our calculation which includes the spin-orbit interaction and the curvature of the nanotubes shows the spin-dependent energy splitting having diameter and chirality dependence, and the asymmetric splitting between the conduction and valence bands. An effective model at the Dirac points is derived using second order perturbation theory for the spin-orbit interaction and curvature. The calculation explains the experiment well. For both cases, the curvature significantly induces the new effects from their corresponding plane structure.
16.02.2011
Prof. Dr. Mark M. Malamud; (Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine)
On the unitary equivalence of absolutely continuous parts of self-adjoint extensions