环境为热浴的开放量子系统模型的研究

J4 ›› 2011, Vol. 28 ›› Issue (6): 660-673.

环境为热浴的开放量子系统模型的研究

杨洁, 丛爽

中国科学技术大学自动化系, 安徽合肥, 230026

收稿日期:2010-10-25 修回日期:2011-01-10 出版日期:2011-11-28 发布日期:2011-11-14
通讯作者: 丛爽（1961- ）女，山东文登人，博士，教授，博士生导师，现主要从事人工神经网络、模糊神经系统、运动控制、智能控制、量子系统控制等方向的研究。 E-mail:scong@ustc.edu.cn
作者简介:杨洁（1983-）女，浙江绍兴人，博士，主要从事开放量子建模及其控制方面的研究。 E-mail: yjie712@mail.ustc.edu.cn
基金资助:
国家重点基础研究发展计划（973）（2009CB929601）、国家自然科学基金（61074050）和中国科学技术大学研究生创新基金资助项目。

Research on models of open quantum system interacted with bath

YANG Jie, CONG Shuang

Department of Automation, University of Science and Technology of China, Hefei 230026, China

Received:2010-10-25 Revised:2011-01-10 Published:2011-11-28 Online:2011-11-14

摘要/Abstract

摘要：

基于具有non-Markovian特性的关于量子系统约化密度矩阵的精确系统动力学方程，分别根据方程所具有的非封闭、不等时、积分微分方程的特性，通过Born逼近和Markov逼近得到关于量子系统约化密度矩阵的封闭、等时和微分的Markovian主方程；逐一分析了Markovian主方程的Lindblad形式、具有方便检验正定性的GKS表达形式、针对单量子位系统的Bloch球表达形式和无需明确的环境信息也能对开放系统进行描述的Kraus表达形式；分析并比较了能去除系统动力学方程non-Markovian特性的4种Markov逼近方法以及其他四种特定情形下常见的Markovian主方程；对于不适用于Markov逼近的情形，分析了能满足开放量子系统动力学对于系统状态要求的post-Markovian主方程；当热浴与量子系统发生能量交换，且热浴与量子系统组成的封闭系统能量守恒时，给出了热浴状态不恒定时开放量子系统的动力学方程，并通过Markov逼近得到Markovian主方程。

关键词: 量子光学, 开放量子系统, Markov逼近, Markovian主方程, non-Markovian主方程

Abstract:

Based on the exact non-Markovian system dynamic equation about the reduced density matrix of quantum system, which is a non-closed, unequal in time, integral-differential equation, we derived a closed, equal in time, differential Markovian master equation about the reduced density matrix of quantum system by means of Born approximation and Markov approximation. The Lindblad form of the Markovian master equation, the GKS expression for the convenience of testing positivity, the Bloch sphere expression for single qubit system, the Kraus expression describing dissipative quantum system without specific information of environment were analyzed respectively. Four kinds of Markov approximations that can remove the non-Markovian property were compared. We analyzed the post-Markovian master equation that can meet the perfect requirements of dissipative dynamic when the Markov approximation is not suitable to the open quantum system. When energy exchange is existed between the heat bath and the quantum system, while the total system composed of the bath and the quantum system has a conservation of energy, we presented the dynamic equation of open quantum system when the bath does not have a constant state, and the Markovian master equation was derived by the Markov approximation.

Key words: quantum optics, open quantum system, Markov approximation, Markovian master equation, non-Markovian master equation

中图分类号:

O411
TP15

杨洁丛爽. 环境为热浴的开放量子系统模型的研究[J]. J4, 2011, 28(6): 660-673.

YANG Jie, CONG Shuang. Research on models of open quantum system interacted with bath[J]. J4, 2011, 28(6): 660-673.

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