Mathematical and Theoretical Physics Seminar (MTPS)

Jakob Möller (University of Vienna)

Velocity Averaging for the Wigner equation

Abstract: Velocity averaging is an important tool in the theory of kinetic equations because it provides additional regularity for averages of the phase space density in the velocity variable. This is a crucial step e.g. in the proof of the existence of global weak solutions of the Vlasov-Maxwell equation. The Wigner equation is a quantum kinetic equation for the Wigner transform of a density matrix, therefore it is natural to ask whether velocity averaging applies in the quantum case. I will present some recent work in collaboration with F. Golse (CMLS, École Polytechnique).

Joost de Nijs (TU Delft)

Feynmann influence functional approach to system-(coherent) bath dynamics

Abstract: Open quantum systems where the bath consists of a coherent state are of broad interest in quantum optics, as shown in laser physics for example. In contrast, this formalism has only recently been imported to solid state physics, now coined Quantum Acoustics, by applying it to the Fröhlich Hamiltonian. For a large bath, however, simulating such a system naively gets exponentially more expensive, thus rendering a mean field approach as effectively the only game in town. Here we instead open up an unexpolered path guided by Feynmann's footsteps: In particular, we determine the influence functional for such a system, shedding light onto the ambiguous difference between the exact and mean-field dynamics. A stochastic Liouville-von Neumann equation can then be obtained by transforming the influence functional, which allows us to simulate large baths in an exact manner. This framework is then applied to lattice vibrations in real materials to demonstrate the effectiveness of method.

Andrew Rout (University of Rennes)

Title TBA

Abstract: TBA