- Montag, 25.09.2023, 10:00 Uhr (WIAS-ESH)
- Seminar Materialmodellierung
Leonardo Araujo, Technische Universität München:
Beyond the Born--Oppenheimer approximation by Surface Hopping Trajectories methods
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal
In molecular dynamics, the Born--Oppenheimer approximation is a fundamental concept, assuming the decoupling of electronic and nuclear motions due to the significant mass difference between them. This implies that, from the perspective of the nuclei, the electrons effectively reside in an eigenstate. While this approximation is widely employed in quantum chemistry to expedite molecular wavefunction calculations, it encounters limitations, especially in scenarios involving light atoms and high-energy systems. In the first part of this presentation, we confront this limitation by going beyond the Born--Oppenheimer approximation and adding multiple electronic eigenstates into the approximation. We will discuss the theory of this approach and present the resulting equations of motion for the nuclei. Moving on to the second part, we explore computationally efficient methods for simulating such dynamics by considering a class of quantum-classical methods: the Surface Hopping Trajectories. These methods entail an ensemble of trajectories, sampled from the initial nuclear configuration, performing classical dynamics on the eigensurface of an electronic eigenstate. They further allow each trajectory to undergo transitions to different eigenstates guided by hopping probabilities. We present two famous versions of Surface Hopping: the Fewest-Switches Surface Hopping (FSSH) and the Single Switch Surface Hopping (SSSH), also recognised as Landau--Zener Surface Hopping. To culminate, we illustrate the use of these methods through a practical example using WavePacket, a Matlab software package for quantum-mechanical and quantum-classical simulations.
- Mittwoch, 27.09.2023, 11:30 Uhr (WIAS-405-406)
- Seminar Interacting Random Systems
Michiel Renger, TU München:
Collisions in the exclusion process
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406
The simple symmetric exclusion process (SSEP) and a system of independent random walkers both converge to the same diffusion equation. To understand the difference, we count the number of times a SSEP particle would have jumped if the particles were independent, but did not jump because the target site was occupied. This number can also be interpreted as the number of times two SSEP particles collide. We show its hydrodynamic limit using Markov duality. In fact, we are interested in a whole zoo of related microscopic variables, and if time allows I will briefly talk about their large deviations. Ongoing work with Mario Ayala (TUM).
Seminar Interacting Random Systems (Hybrid Event)