In this document we discuss the long time behaviour for the homogeneous Landau-Fermi-Dirac equation in the hard potential case. Uniform in time estimates for statistical moments and Sobolev regularity are presented and used to prove exponential relaxation of non degenerate distributions to the Fermi-Dirac statistics. All these results are valid for rather general initial datum. An important feature of the estimates is the independence with respect to the quantum parameter. Consequently, in the classical limit the same estimates are recovered for the Landau equation.

中文翻译：

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具有硬势的 Landau-Fermi-Dirac 方程的长时间动力学

在本文档中，我们讨论了在硬势情况下齐次 Landau-Fermi-Dirac 方程的长时间行为。呈现了对统计矩和 Sobolev 规律的统一时间估计，并用于证明非简并分布对 Fermi-Dirac 统计的指数松弛。所有这些结果对于相当一般的初始数据都是有效的。估计的一个重要特征是相对于量子参数的独立性。因此，在经典极限中，可以恢复朗道方程的相同估计值。