Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
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DOI：
10.1016/j.aop.2010.12.003
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发表时间：
2011-05-01
影响因子：
3
通讯作者：
Hu, B. L.
中科院分区：
文献类型：
--
作者：
Fleming, C. H.;Roura, Albert;Hu, B. L.
我们重新审视在有限温度下与量子振荡器环境线性耦合的量子布朗振荡器模型。通过引入一个紧凑且特别适合的公式，我们给出了主方程及其针对一般光谱函数和任意温度的解的相当快速和直接的推导。我们方法的灵活性允许立即推广到具有外力和任意数量的布朗振荡器的情况。更重要的是，我们指出了关于积分微分方程边值问题的一个重要的数学微妙之处，它导致了不正确的主方程系数，并影响了所有早期推导中非局部耗散效应的描述。此外，我们还为各种情况下的主方程系数及其解提供了明确、准确的分析结果，包括具有有限截止的欧姆、亚欧姆和超欧姆环境。由爱思唯尔公司出版
We revisit the model of a quantum Brownian oscillator linearly coupled to an environment of quantum oscillators at finite temperature. By introducing a compact and particularly well-suited formulation, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. The flexibility of our approach allows for an immediate generalization to cases with an external force and with an arbitrary number of Brownian oscillators. More importantly, we point out an important mathematical subtlety concerning boundary-value problems for integro-differential equations which led to incorrect master equation coefficients and impacts on the description of nonlocal dissipation effects in all earlier derivations. Furthermore, we provide explicit, exact analytical results for the master equation coefficients and its solutions in a wide variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with a finite cut-off. Published by Elsevier Inc.