论文标题
纯粹的稳态和赌徒的废墟问题的耗散产生
Dissipative generation of pure steady states and a gambler's ruin problem
论文作者
论文摘要
我们考虑一个开放的量子系统，耗散仅应用于其自由度的一部分，并通过量子马尔可夫动力学发展。我们证明，在大耗散的ZENO机制中，量子系统向纯量子状态的松弛与经典马尔可夫过程向单个吸收状态的演变有关。相关的经典马尔可夫过程的速率由原始量子动力学决定。将该对应关系扩展到具有内部结构的吸收状态，使我们能够建立一个通用标准，即具有任意有限级的Zeno-Limit非平衡固定状态。在开放的XXZ Spin-1/2链中，该标准的应用说明了其边缘的开放XXZ Spin-1/2链与具有固定和不同极化的浴室。对于此系统，我们发现了等级1和2的确切非平衡稳态解决方案。
We consider an open quantum system, with dissipation applied only to a part of its degrees of freedom, evolving via a quantum Markov dynamics. We demonstrate that, in the Zeno regime of large dissipation, the relaxation of the quantum system towards a pure quantum state is linked to the evolution of a classical Markov process towards a single absorbing state. The rates of the associated classical Markov process are determined by the original quantum dynamics. Extension of this correspondence to absorbing states with internal structure allows us to establish a general criterion for having a Zeno-limit nonequilibrium stationary state of arbitrary finite rank. An application of this criterion is illustrated in the case of an open XXZ spin-1/2 chain dissipatively coupled at its edges to baths with fixed and different polarizations. For this system, we find exact nonequilibrium steady-state solutions of ranks 1 and 2.
