Communications in Mathematical Sciences
Volume 5 (2007)
Supplemental Issue 1
A Short Review on the Derivation of the Nonlinear Quantum Boltzmann Equations
Pages: 55 – 71
In this review paper we describe the problem of deriving a Boltzmann equation for a system of $N$ interacting quantum particles, under the appropriate scaling limits. We mainly follow the approach developed by the authors in previous works. From a rigorous viewpoint, only partial results are available, even for short times, so that the complete problem is still open.
Kinetic equations; quantum systems; weak coupling; low density; stationary phase
2010 Mathematics Subject Classification