含运动积分的热化开放量子系统的热力学第零定律
Zeroth law of thermodynamics for thermalized open quantum systems having integrals of motion
摘要：
研究了以Lindblad超算子为生成元的动力学半群所描述的开放量子系统的演化。该发生器可以具有被称为运动常数（COM）的具有单位本征值的本征函数。一个开放量子系统有唯一的定态当且仅当它没有COM。具有多个定态的系统具有COM的基;系统的任何COM是基本COM的线性组合。基将系统状态空间划分为子空间。每个子空间都有自己的定态，系统的任何定态都是这些状态的线性组合。通常，既不知道COM的基础，也不知道COM的数量。我们证明，找到系统的稳态不需要寻找的COM。相反，可以构造一组不变子空间。如果系统的演化从这些子空间中的一个开始，系统将保持在其中，到达一个与其他子空间中的演化无关的稳态。我们提出了一个直接的方法来寻找不变子空间的研究系统的发展。我们证明了不变子空间和由COM基生成的子空间的集合是等价的。系统的稳态是每个不变子空间中稳态的加权和;加权因子由系统的初始状态确定。
英文摘要：
We study the evolution of an open quantum system described by a dynamical semigroup having the Lindblad superoperator as a generator. This generator may have an eigenfunction with a unity eigenvalue, referred to as a constant of motion (COM). An open quantum system has a unique stationary state if and only if it has no COMs. A system with multiple stationary states has a basis of COMs; any COM of the system is a linear combination of the basis COMs. The basis divides the space of system states into subspaces. Each subspace has its own stationary state, and any stationary state of the system is a linear combination of these states. Usually, neither the basis of COMs nor even the number of COMs is known. We demonstrate that finding the stationary state of the system does not require looking for the COMs. Instead, one can construct a set of invariant subspaces. If the system evolution begins from one of these subspaces, the system will remain in it, arriving at a stationary state independent of evolution in other subspaces. We suggest a direct way of finding the invariant subspaces by studying the evolution of the system. We show that the sets of invariant subspaces and subspaces generated by the basis of COMs are equivalent. A stationary state of the system is a weighted sum of stationary states in each invariant subspace; the weighted factors are determined by the initial state of the system.
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