Derivation of Nonlinear Quantum Boltzmann Equation (B02)

Subject Area Mathematics
Term since 2023
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 470903074
 

Project Description

Studied are fermions on a lattice with an interaction strength $\lambda$. For a spatially homogeneous initial state, the goal is to prove the validity of a kinetic equation for the momentum distribution on the time scale $\lambda^{-2}$. Two distinct approaches are envisioned. (i) Diagrammatic expansions involving high-dimensional oscillatory integrals of any order and (ii) Bosonization for a more effective control of error terms.
DFG Programme CRC/Transregios
Subproject of TRR 352:  Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
Applicant Institution Ludwig-Maximilians-Universität München
Project Heads Professor Dr. Phan Thanh Nam; Professor Dr. Herbert Spohn