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arXiv 1407.0129quant-phphysics.chem-ph
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任意耦合强度下两个全同量子振子的准平衡弛豫

Quasi-equilibrium relaxation of two identical quantum oscillators with arbitrary coupling strength

Illarion Dorofeyev

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24 pages, 5 figures
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摘要：

本文研究开放系统的非平衡问题。利用路径积分方法，导出了任意耦合全同量子振子与独立库相互作用系统的含时密度矩阵的解析表达式.的时间行为的空间方差和协方差从给定的初始值到固定值进行了研究。结果表明，在相对较低的耦合强度的渐近方差在长时间的极限达到稳定状态，尽管在初始条件。方差的固定值不同于总平衡的情况下，由于它们的耦合同时与不同温度的热储。热浴温差越大，耦合振子方差的定态值与涨落耗散定理给出的值的差异越大。在强耦合下，方差具有发散性。另外，在弱耦合极限下，尽管整个系统内部温度不同，渐近平稳方差总是符合涨落耗散定理。

英文摘要：

The paper deals with the problem of open systems out of equilibrium. An analytical expression for time-dependent density matrix of two arbitrary coupled identical quantum oscillators interacting with separate reservoirs is derived using path integral methods. The temporal behavior of spatial variances and of covariance from given initial values up to stationary values is investigated. It was shown that at comparatively low coupling strengths the asymptotic variances in the long-time limit achieve steady states despite on initial conditions. Stationary values of variances differ from the case of total equilibrium due to their coupling simultaneously with thermal reservoirs of different temperatures. The larger the difference in temperatures of thermal baths, the larger is the difference of the stationary values of variances of coupled oscillators comparing with values given by the fluctuation dissipation theorem. At strong couplings the variances have divergent character. Otherwise, in the weak coupling limit the asymptotic stationary variances are always in accordance with the fluctuation dissipation theorem despite of the difference in temperatures within the whole system.

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