ON THE WEAK-COUPLING LIMIT FOR BOSONS AND FERMIONS
ON THE WEAK-COUPLING LIMIT FOR BOSONS AND FERMIONS
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DOI：
10.1142/s0218202505000984
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发表时间：
2005-03
影响因子：
3.5
通讯作者：
D. Benedetto;François Castella;R. Esposito;M. Pulvirenti
中科院分区：
文献类型：
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作者：
D. Benedetto;François Castella;R. Esposito;M. Pulvirenti
在本文中，我们考虑一个大系统的玻色子或费米子。我们从一个与玻色-爱因斯坦统计和费米-狄拉克统计相容的初始数据开始。我们让相互作用的粒子系统在弱耦合状态下演化。我们表明，在极限，并高达二阶的潜力，微扰的扩展表示的值的单粒子维格纳函数在时间t，同意类似的扩展的解决方案的Uehling-Uhlenbeck方程。本文遵循与同伴工作相同的精神，2其中作者研究了服从麦克斯韦-玻尔兹曼统计的粒子的弱耦合极限：在这里，他们证明了一个（更强）的玻尔兹曼方程解的收敛结果。
In this paper we consider a large system of bosons or fermions. We start with an initial datum which is compatible with the Bose–Einstein, respectively Fermi–Dirac, statistics. We let the system of interacting particles evolve in a weak-coupling regime. We show that, in the limit, and up to the second order in the potential, the perturbative expansion expressing the value of the one-particle Wigner function at time t, agrees with the analogous expansion for the solution to the Uehling–Uhlenbeck equation. This paper follows the same spirit as the companion work,2 where the authors investigated the weak-coupling limit for particles obeying the Maxwell–Boltzmann statistics: here, they proved a (much stronger) convergence result towards the solution of the Boltzmann equation.