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arXiv 0906.4288quant-ph
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马尔可夫开放系统的复杂WKB演化

Complex WKB Evolution of Markovian Open Systems

O. Brodier, A. M. Ozorio de Almeida

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16 pages
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摘要：

作为复WKB理论的推广，我们导出了由林德布拉德方程产生的演化的半经典近似。假设与环境的线性耦合，但哈密顿量可以是位置和动量的一般函数。该理论在弦表象中进行，并描述了演化的量子特征函数，该特征函数通过傅立叶变换直接获得Wigner函数和密度算符的位置表象。的传播示出的刘维尔型在一个复杂的双相空间，虚部的行动负责退相干。该理论在二次情形下是精确的，就像我们以前为扩展态的马尔可夫演化开发的真实WKB理论一样，但它也描述了局域态的退相干和耗散演化，例如薛定谔猫态的干涉项。本rederivative的真实WKB近似导致其解释为一阶经典微扰的复杂理论和讨论其有效性。一个简单的三次哈密顿量的例子说明了从复杂的WKB理论推导出的各种近似水平。

英文摘要：

We derive a semiclassical approximation for the evolution generated by the Lindblad equation as a generalization of complex WKB theory. Linear coupling to the environment is assumed, but the Hamiltonian can be a general function of positions and momenta. The theory is carried out in the chord representation and describes the evolved quantum characteristic function, which gives direct access to the Wigner function and the position representation of the density operator by Fourier transforms. The propagation is shown to be of Liouville type in a complex double phase space, the imaginary part of the action being responsible for decoherence. The theory is exact in the quadratic case, just as the real WKB theory that we previously developed for the Markovian evolution of extended states, but it also describes the decoherent and dissipative evolution of localized states, such as the interference terms of a Schrödinger cat state. The present rederivation of the real WKB approximation leads to its interpretation as a first order classical perturbation of the complex theory and to a discussion of its validity. The example of a simple cubic Hamiltonian illustrates the various levels of approximation derived from the complex WKB theory.

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