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



D. Benedetto

F. Castella

R. Esposito

M. Pulvirenti


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

82C10, 82C40

Full Text (PDF format)