Derivation of Nonlinear Quantum Boltzmann Equation (B02)

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

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