关于有耗散和无耗散白噪声哈密顿的平均量子动力学
On the averaged quantum dynamics by white-noise Hamiltonians with and without dissipation
摘要：
给出了一类随机量子动力系统在连续空间中的平均动力学的精确结果。类的每个成员都由一个哈密顿量来表征，该哈密顿量是两个部分的和。其中一部分是确定性的、时间无关的和二次的，而另一部分的Weyl-Wigner符号是一个均匀的高斯随机场，它在时间上是δ相关的，但在位置和动量上是平滑相关的。所得到的白噪声系统的平均动力学被证明是一个单调混合递增的量子动力学半群。它的生成器是显式计算的。通常，随着时间的推移，这样一个系统的平均能量线性增长到无穷大。在本文的第二部分中的扩展模型进行了研究，其中，此外，占耗散耦合的白噪声系统线性量子力学谐波热浴。它表明，在适当的假设下的频谱密度的热浴，平均能量，然后饱和很长一段时间。
英文摘要：
Exact results are derived on the averaged dynamics of a class of random quantum-dynamical systems in continuous space. Each member of the class is characterized by a Hamiltonian which is the sum of two parts. While one part is deterministic, time-independent and quadratic, the Weyl-Wigner symbol of the other part is a homogeneous Gaussian random field which is delta correlated in time, but smoothly correlated in position and momentum. The averaged dynamics of the resulting white-noise system is shown to be a monotone mixing increasing quantum-dynamical semigroup. Its generator is computed explicitly. Typically, in the course of time the mean energy of such a system grows linearly to infinity. In the second part of the paper an extended model is studied, which, in addition, accounts for dissipation by coupling the white-noise system linearly to a quantum-mechanical harmonic heat bath. It is demonstrated that, under suitable assumptions on the spectral density of the heat bath, the mean energy then saturates for long times.
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