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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:经典和量子系统中非平衡的方面:缓慢   放松和眼镜,动态大偏差,量子非遍历性,   和开放量子动力学

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摘要

In these four lectures I describe basic ideas and methods applicable to bothclassical and quantum systems displaying slow relaxation and non-equilibriumdynamics. The first half of these notes considers classical systems, and thesecond half, quantum systems. In Lecture 1, I briefly review the glasstransition problem as a paradigm of slow relaxation and dynamical arrest inclassical many-body systems. I discuss theoretical perspectives on how to thinkabout glasses, and in particular how to model them in terms of kineticallyconstrained dynamics. In Lecture 2, I describe how via large deviation methodsit is possible to define a statistical mechanics of trajectories which revealsthe dynamical phase structure of systems with complex relaxation such asglasses. Lecture 3 is about closed (i.e. isolated) many-body quantum systems. Ireview thermalisation and many-body localisation, and consider the possibilityof 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 aboutopen quantum systems, that is, quantum systems interacting with an environment.I review the description of open quantum dynamics within the Markovianapproximation in terms of quantum master equations and stochastic quantumtrajectories, and explain how to extend the dynamical large deviation method tostudy the statistical properties of ensembles of quantum jump trajectories. Myoverall aim is to draw analogies between classical and quantum non-equilibriumand find connections in the way we think about problems in these areas.
机译:在这四个讲座中,我描述了适用于显示慢弛豫和非平衡动力学的经典系统和量子系统的基本思想和方法。这些注释的前半部分考虑经典系统,后半部分考虑量子系统。在第1课中,我简要回顾了玻璃化转变问题,将其作为经典多体系统中的缓慢弛豫和动态停滞的范例。我讨论了有关如何思考眼镜的理论观点,尤其是如何根据动力学约束的动力学对它们进行建模。在第2课中,我描述了如何通过大偏差方法来定义轨迹的统计力学,从而揭示具有复杂弛豫的系统(如玻璃)的动态相结构。第3课是关于封闭的(即孤立的)多体量子系统的。我回顾了热化和多体定位,并考虑了在没有无序的情况下缓慢热化和量子非遍历性的可能性,从而与第一堂课的一些思想联系在一起。第4讲是关于开放量子系统的,即与环境相互作用的量子系统。量子跃迁轨迹的统计特性。我的总体目标是在经典与量子非平衡之间进行类比,并以我们思考这些领域中问题的方式找到联系。

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    Garrahan, Juan P.;

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