A short review on the derivation of the nonlinear quantum Boltzmann equations

被引：0

作者：

Benedetto, D.

Castella, F.

Esposito, R.

Pulvirenti, M.

机构：

[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy

[2] Univ Rennes 1, IRMAR, F-35042 Rennes, France

[3] Univ Aquila, Dipartimento Matemat Pura & Applicata, I-67100 Laquila, Italy

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2007年 / 5卷

关键词：

kinetic equations; quantum systems; weak coupling; low density; stationary phase;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：55 / 71

页数：17

共 19 条

[1]

Balescu R., 1975, Equilibrium and Nonequilibrium Statistical Mechanics

[2] Some considerations on the derivation of the nonlinear quantum Boltzmann equation II: The low density regime [J].