Institute of Physics, University of Silesia, 40-007 Katowice, Poland.
Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland.
Phys Rev E. 2017 May;95(5-1):052137. doi: 10.1103/PhysRevE.95.052137. Epub 2017 May 23.
The statistics of work performed on a system by a sudden random quench is investigated. Considering systems with finite dimensional Hilbert spaces we model a sudden random quench by randomly choosing elements from a Gaussian unitary ensemble (GUE) consisting of Hermitian matrices with identically, Gaussian distributed matrix elements. A probability density function (pdf) of work in terms of initial and final energy distributions is derived and evaluated for a two-level system. Explicit results are obtained for quenches with a sharply given initial Hamiltonian, while the work pdfs for quenches between Hamiltonians from two independent GUEs can only be determined in explicit form in the limits of zero and infinite temperature. The same work distribution as for a sudden random quench is obtained for an adiabatic, i.e., infinitely slow, protocol connecting the same initial and final Hamiltonians.
研究了系统受到突发随机淬火时的工作统计。考虑具有有限维 Hilbert 空间的系统，我们通过从具有相同、高斯分布矩阵元素的 Hermitian 矩阵组成的高斯幺正系综 (GUE) 中随机选择元素来模拟突发随机淬火。针对两能级系统，导出了工作的概率密度函数 (pdf) 与初始和最终能量分布之间的关系，并进行了评估。对于具有给定初始哈密顿量的淬火，我们得到了显式结果，而对于来自两个独立 GUE 的哈密顿量之间的淬火，只有在零温极限和无穷温极限下才能以显式形式确定工作 pdf。对于连接相同初始和最终哈密顿量的绝热、即无限缓慢的协议，我们得到了与突发随机淬火相同的工作分布。
