Contents Online
Communications in Mathematical Sciences
Volume 5 (2007)
Supp. 1
Supplemental Issue 1
A Short Review on the Derivation of the Nonlinear Quantum Boltzmann Equations
Pages: 55 – 71
DOI: https://dx.doi.org/10.4310/CMS.2007.v5.n5.a5
Authors
Abstract
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.
Keywords
Kinetic equations, quantum systems, weak coupling, low density, stationary phase
2010 Mathematics Subject Classification
82C10, 82C40
Published 1 January 2007