Tsai Hung-Ming, Müller Berndt
Department of Physics, Duke University, Durham, North Carolina 27708, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jan;85(1 Pt 1):011110. doi: 10.1103/PhysRevE.85.011110. Epub 2012 Jan 5.
The Husimi distribution provides for a coarse-grained representation of the phase-space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving the Husimi equation of motion for an isolated quantum system, and we construct a coarse-grained Hamiltonian whose expectation value is exactly conserved. As an application, we numerically solve the Husimi equation of motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and calculate the time evolution of the coarse-grained entropy of a highly excited state. We show that the coarse-grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system.
胡西米分布提供了量子系统相空间分布的粗粒化表示，可用于追踪系统熵的增长。我们提出了一种求解孤立量子系统胡西米运动方程的通用且系统的方法，并构建了一个粗粒化哈密顿量，其期望值严格守恒。作为应用，我们对二维杨-米尔斯量子力学（x-y模型）的胡西米运动方程进行了数值求解，并计算了高激发态粗粒化熵的时间演化。我们表明，粗粒化熵会饱和到一个与对应于系统能量的微正则熵相一致的值。
