Biele R, Timm C, D'Agosta R
ETSF Scientific Development Center, Departamento de Física de Materiales, Universidad del País Vasco, E-20018 San Sebastián, Spain. Institute of Theoretical Physics, Technische Universität Dresden, D-01062 Dresden, Germany.
J Phys Condens Matter. 2014 Oct 1;26(39):395303. doi: 10.1088/0953-8984/26/39/395303. Epub 2014 Sep 10.
Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the master-equation approach, which is numerically expensive for large dimensions of the Hilbert space. Here, we numerically investigate the suitability of a known stochastic Schrödinger equation that is local in time to give a description of thermal relaxation and energy transport. This stochastic Schrödinger equation can be solved with a moderate numerical cost, indeed comparable to that of a Markovian system, and reproduces the dynamics of a system evolving according to a general non-Markovian master equation. After verifying that it describes thermal relaxation correctly, we apply it for the first time to the energy transport in a spin chain. We also discuss a portable algorithm for the generation of the coloured noise associated with the numerical solution of the non-Markovian dynamics.
基于有效波函数的量子随机方法构成了一个用于研究与热库耦合的量子力学系统一般非马尔可夫动力学的框架。它们有望在计算上优于主方程方法，后者对于大维度希尔伯特空间在数值计算上成本高昂。在此，我们通过数值研究一个时间局部的已知随机薛定谔方程用于描述热弛豫和能量传输的适用性。这个随机薛定谔方程可以以适度的数值成本求解，实际上与马尔可夫系统相当，并且能够重现根据一般非马尔可夫主方程演化的系统动力学。在验证其能正确描述热弛豫之后，我们首次将其应用于自旋链中的能量传输。我们还讨论了一种用于生成与非马尔可夫动力学数值解相关的有色噪声的便携式算法。
