Riera-Campeny Andreu, Sanpera Anna, Strasberg Philipp
Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain.
ICREA, Psg. Lluís Companys 23, 08001 Barcelona, Spain.
Phys Rev E. 2022 May;105(5-1):054119. doi: 10.1103/PhysRevE.105.054119.
An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium but it induces a dynamical evolution of the bath state. In this paper, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equations that improve their accuracy by including more dynamical information of the bath. For instance, as the least accurate but simplest description in the hierarchy, we obtain the conventional Born-Markov-secular master equation. Remarkably, our framework works even if the measurements of the bath energy are imperfect, which not only is more realistic but also unifies the theoretical description. Also, we discuss this formalism in detail for a particular noninteracting environment where the Boltzmann temperature and the Kubo-Martin-Schwinger relation naturally arise. Finally, we apply our hierarchy of master equations to study the central spin model.
一个与无限大的热库接触的开放量子系统会趋向于平衡，而热库的状态保持不变。如果热库是有限的，开放系统仍然会弛豫到平衡，但它会引起热库状态的动力学演化。在本文中，我们研究了与有限热库接触的开放量子系统的动力学。我们得到了一组主方程层级，通过纳入热库更多的动力学信息来提高其准确性。例如，作为层级中最不准确但最简单的描述，我们得到了传统的玻恩 - 马尔可夫 - 久期主方程。值得注意的是，即使对热库能量的测量不完美，我们的框架仍然有效，这不仅更符合实际情况，而且统一了理论描述。此外，我们针对一个特定的非相互作用环境详细讨论了这种形式体系，在该环境中自然会出现玻尔兹曼温度和久保 - 马丁 - 施温格关系。最后，我们应用我们的主方程层级来研究中心自旋模型。
