论文标题
有限状态空间的Lindblad方程固定状态的显式表达式
Explicit expressions for stationary states of the Lindblad equation for a finite state space
论文作者
论文摘要
Lindblad方程描述了量子机械系统密度矩阵的时间演变。固定溶液是通过时间平衡溶液获得的，该溶液通常取决于初始状态。我们使用量子跳跃分解，沿旧定理的版本以及相应的离散时间马尔可夫链的固定概率为Lindblad方程的稳态提供了分析表达式。当出现量子轨迹的状态数量有限时，我们的结果是有效的。马尔可夫跳跃过程的经典案例被恢复为一种特殊情况，并讨论了两者之间的差异。
The Lindblad equation describes the time evolution of a density matrix of a quantum mechanical system. Stationary solutions are obtained by time-averaging the solution, which will in general depend on the initial state. We provide an analytical expression for the steady states of the Lindblad equation using the quantum jump unraveling, a version of an ergodic theorem, and the stationary probabilities of the corresponding discret-time Markov chains. Our result is valid when the number of states appearing the in quantum trajectory is finite. The classical case of a Markov jump-process is recovered as a special case, and differences between the two are discussed.
