arXiv quant-ph/02080942002-08-14quant-ph

半经典Wigner函数的退相干

Decoherence of Semiclassical Wigner Functions

Alfredo M. Ozorio de Almeida

备注：: 23 pg, 2 fig
DOI：: 10.1088/0305-4470/36/1/305

摘要：

林德布拉德方程支配开放量子系统中密度算符的一般马尔可夫演化。维格纳函数的变化率的表达式作为积分之和是该方程的外尔表示的形式之一。维格纳函数的弦的半经典描述，每个弦都有其经典定义的振幅和相位，因此插入积分中，这导致维格纳函数的显式微分方程。所有的Lindblad算子被假定为对应于经典变量的光滑相空间函数。在这些都是真实的情况下，代表厄米算子，半经典林德布拉德方程可以集成。结果是半经典维格纳函数的幺正演化的一个简单的扩展，它不影响每个弦贡献的相位，同时抑制其振幅。这呈指数下降，由Lindblad函数的平方差的时间积分沿着每个弦的两个尖端的经典轨迹支配。振幅的衰减表明，意味着扩散的初始状态，几乎是纯的能量。将维格纳函数投影到正交位置或动量基上，长弦的阻尼表现为密度矩阵的非对角元素的指数衰减。

英文摘要：

The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation for this equation. The semiclassical description of the Wigner function in terms of chords, each with its classically defined amplitude and phase, is thus inserted in the integrals, which leads to an explicit differential equation for the Wigner function. All the Lindblad operators are assumed to be represented by smooth phase space functions corresponding to classical variables. In the case that these are real, representing hermitian operators, the semiclassical Lindblad equation can be integrated. There results a simple extension of the unitary evolution of the semiclassical Wigner function, which does not affect the phase of each chord contribution, while dampening its amplitude. This decreases exponentially, as governed by the time integral of the square difference of the Lindblad functions along the classical trajectories of both tips of each chord. The decay of the amplitudes is shown to imply diffusion in energy for initial states that are nearly pure. Projecting the Wigner function onto an orthogonal position or momentum basis, the dampening of long chords emerges as the exponential decay of off-diagonal elements of the density matrix.

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