二能级系统的马尔可夫与非马尔可夫方法比较  

Comparison of Markovian and non-Markovian methods for two-level system

作　　者：王小云[1] 邓科[1] 吴利华[1] 李德俊[1] 赵鹤平[1] 

机构地区：[1]吉首大学物理与机电工程学院,湖南吉首416000

出　　处：《强激光与粒子束》2012年第5期1160-1164,共5页High Power Laser and Particle Beams

基　　金：湖南省自然科学基金项目(09JJ6011;11JJ6007);湖南省教育厅项目(10A100;11C1057)

摘　　要：分别用马尔可夫与非马尔可夫方法推导出二能级系统与库相互作用的耗散动力学,并把失谐谱密度与一个光子带隙的谱密度下的计算结果与精确解进行比较。对于失谐谱密度,分别讨论在马尔可夫与非马尔可夫库的激发态布居数,发现无论是短时的弱耦合区域,还是长时间的强耦合区域,非马尔可夫方法比马尔可夫方法更加接近精确解,而马尔可夫近似主要适用于弱耦合条件;对于光子带隙谱密度,主要考虑了小带宽的布居数,结果显示马尔可夫方法主要适用于弱耦合条件,而非马尔可夫方法主要适用于强耦合情形。结果表明:对于不同谱密度、不同的耦合区域,只有选择合适的马尔可夫或非马尔可夫方法才能精确描述系统的动力学。The dissipative dynamics of a two-level system interacting with a reservoir has been solved by Markovian and nonMarkovian approaches.The results in conditions of two different spectral densities,namely the detuning spectral density and a photonic gap distributed density,are compared with the exact solutions.In the first case,the population of excitation state in the non-Markovian and Markovian reservoirs is discussed.For both weak coupling regime in short time and a long period of strong coupling regime,the result of non-Markovian approaches is more consistent with the exact solution,while the Markovian approximation is mainly applicable to weak coupling condition.In the second case,the population in small gap width is considered.The Markovian approach is applied in weak coupling condition,but in strong condition the non-Markovian approximation is exploited.Therefore,through appropriate choice of Markovian and non-Markovian approaches,the dynamics of a system can be described exactly for different spectral densities and coupling regimes.

关 键 词：复杂系统 马尔可夫方程 非马尔可夫主方程 关联函数 谱密度 

分 类 号：O431.2[机械工程—光学工程]