School of Physics and Astronomy, The University of Nottingham, Nottingham, United Kingdom.
Phys Rev Lett. 2012 Mar 16;108(11):110603. doi: 10.1103/PhysRevLett.108.110603. Epub 2012 Mar 14.
Thermalization has been shown to occur in a number of closed quantum many-body systems, but the description of the actual thermalization dynamics is prohibitively complex. Here, we present a model-in one and two dimensions-for which we can analytically show that the evolution into thermal equilibrium is governed by a Fokker-Planck equation derived from the underlying quantum dynamics. Our approach does not rely on a formal distinction of weakly coupled bath and system degrees of freedom. The results show that transitions within narrow energy shells lead to a dynamics which is dominated by entropy and establishes detailed balance conditions that determine both the eventual equilibrium state and the nonequilibrium relaxation to it.
热化已在许多封闭的量子多体系统中得到证实，但对实际热化动力学的描述过于复杂。在这里，我们提出了一个模型——在一维和二维中——我们可以分析证明，进入热平衡的演化是由从基础量子动力学推导出的福克-普朗克方程控制的。我们的方法不依赖于弱耦合浴和系统自由度的正式区分。结果表明，在狭窄的能壳内的跃迁导致一个主要由熵主导的动力学，并建立了确定最终平衡状态和向其非平衡弛豫的详细平衡条件。
