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首页> 外文期刊>Physica, A. Statistical mechanics and its applications >Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics
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Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics

机译：古典和量子系统中非平衡的各个方面：缓和放松和眼镜，动态大的偏差，量子非遍布性和开放量子动态

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In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second half, quantum systems. In Lecture 1, I briefly review the glass transition problem as a paradigm of slow relaxation and dynamical arrest in classical many-body systems. I discuss theoretical perspectives on how to think about glasses, and in particular how to model them in terms of kinetically constrained dynamics. In Lecture 2, I describe how via large deviation methods it is possible to define a statistical mechanics of trajectories which reveals the dynamical phase structure of systems with complex relaxation such as glasses. Lecture 3 is about closed (i.e. isolated) many-body quantum systems. I review thermalisation and many-body localisation, and consider the possibility of slow thermalisation and quantum non-ergodicity in the absence of disorder, thus connecting with some of the ideas of the first lecture. Lecture 4 is about open quantum systems, that is, quantum systems interacting with an environment. I review the description of open quantum dynamics within the Markovian approximation in terms of quantum master equations and stochastic quantum trajectories, and explain how to extend the dynamical large deviation method to study the statistical properties of ensembles of quantum jump trajectories. My overall aim is to draw analogies between classical and quantum non-equilibrium and find connections in the way we think about problems in these areas. (C) 2018 Elsevier B.V. All rights reserved.
机译：在这四个讲座中，我介绍了适用于古典和量子系统的基本思想和方法，显示慢松弛和非平衡动力学。这些笔记的上半部分认为经典系统，下半部分，量子系统。在讲座1中，我简要介绍了玻璃过渡问题作为古典许多身体系统中缓慢放松和动态停滞的范式。我讨论了如何思考眼镜的理论观点，特别是如何在动态受限的动态方面建模它们。在讲座2中，我描述了通过大的偏差方法如何定义轨迹的统计机制，该轨迹揭示了具有复杂松弛的系统的动态相位结构，例如玻璃。讲座3是关于关闭的（即孤立的）许多身体量子系统。我审查了热化和许多身体定位，并考虑了在没有紊乱的情况下慢热化和量子非遍历性的可能性，从而与第一讲座的一些思想连接。讲座4是关于开放量子系统，即量子系统与环境相互作用。我在量子母部方程和随机量子轨迹方面审查了马尔科维亚近似内的开放量子动态的描述，并解释了如何扩展动态大偏差方法，以研究Quantum Jump轨迹集合的统计特性。我的整体目标是在经典和量子非平衡之间绘制类比，并在我们考虑这些地区的问题的方式找到连接。 （c）2018年elestvier b.v.保留所有权利。

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