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阻尼谐振子理论中的纯度和退相干

Purity and decoherence in the theory of a damped harmonic oscillator

A. Isar, A. Sandulescu, W. Scheid

摘要:

对于Karrlein和Grabert导出的阻尼谐振子微观模型的广义主方程,给出了不同初始条件和不同阻尼类型(包括欧姆、Drude和弱耦合情况,Agarwal和Weidlich-Haake模型)下的态纯度条件.结果表明,保持纯态的态是时间方差为常数的压缩态。对于纯态,也得到了与这些主方程对应的广义非线性Schr”odinger型方程.然后在开放量子系统的Lindblad理论框架下讨论了阻尼谐振子的态的纯度条件。对于一个特殊的环境系数的选择,具有恒定的方差和协方差的相关相干态被证明是唯一的状态,保持纯的所有时间在所考虑的系统的发展。在Karrlein-Grabert和Lindblad模型中,以及在所考虑的特殊模型中,给出了熵产生率的表达式,并证明了在时间上保持其纯性的状态也是熵产生最小的状态,因此,它们是在环境存在下演化的最稳定的状态,在描述退相干现象中起着重要的作用。

英文摘要:

For the generalized master equations derived by Karrlein and Grabert for the microscopic model of a damped harmonic oscillator, the conditions for purity of states are written, in particular for different initial conditions and different types of damping, including Ohmic, Drude and weak coupling cases, Agarwal and Weidlich-Haake models. It is shown that the states which remain pure are the squeezed states with constant in time variances. For pure states, the generalized nonlinear Schr\" odinger-type equations corresponding to these master equations are also obtained. Then the condition for purity of states of a damped harmonic oscillator is considered in the framework of Lindblad theory for open quantum systems. For a special choice of the environment coefficients, the correlated coherent states with constant variances and covariance are shown to be the only states which remain pure all the time during the evolution of the considered system. In Karrlein-Grabert and Lindblad models, as well as in the considered particular models, the expressions of the rate of entropy production is written and it is shown that the states which preserve their purity in time are also the states which minimize the entropy production and, therefore, they are the most stable ones under evolution in the presence of the environment and play an important role in the description of decoherence phenomenon.

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