标题： 纯态统计力学：基础及其在量子引力中的应用 显示英文标题

标题： Pure states statistical mechanics: On its foundations and applications to quantum gravity

摘要： 本项目涉及量子力学、统计力学和热力学在孤立量子系统中的相互作用。 其根本目标是提高我们对量子系统中热平衡概念的理解。 首先，我研究了可观测量和测量在热行为出现中所起的作用。 这导致了一个新的热平衡概念，它特定于某个可观测量，而不是系统的整个状态。 由此产生的平衡图景是对统计力学的一种推广，在其中我们不关心系统的状态，而只关心测量过程的结果。 我研究了这种图景如何与孤立量子系统中热行为出现的最有希望的方法之一——本征态热化假设（Eigenstate Thermalization Hypothesis）相关联。 然后，我将这些结果应用于研究多体局域化系统的某些平衡性质。 尽管存在阻止子系统热化的局域化现象，我还是能够表明我们可以仍然使用统计力学的预测来描述某些可观测量的平衡。 此外，在这一过程中发展出的直觉引导我提出了一种实验上可访问的方式来揭示多体局域化系统的相互作用性质。 其次，我利用“集中度量”现象来研究圈量子引力中基态的宏观性质。 这些技术以前被用来解释为什么量子系统中的热行为在宏观尺度上如此普遍。 我专注于局部性质、它们的热力学行为以及与半经典极限的相互作用。 这是由于需要从量子引力的角度理解为什么和如何经典的视界表现出热性质。 显示英文摘要

摘要： The project concerns the interplay among quantum mechanics, statistical mechanics and thermodynamics, in isolated quantum systems. The underlying goal is to improve our understanding of the concept of thermal equilibrium in quantum systems. First, I investigated the role played by observables and measurements in the emergence of thermal behaviour. This led to a new notion of thermal equilibrium which is specific for a given observable, rather than for the whole state of the system. The equilibrium picture that emerges is a generalization of statistical mechanics in which we are not interested in the state of the system but only in the outcome of the measurement process. I investigated how this picture relates to one of the most promising approaches for the emergence of thermal behaviour in isolated quantum systems: the Eigenstate Thermalization Hypothesis. Then, I applied the results to study some equilibrium properties of many-body localised systems. Despite the localization phenomenon, which prevents thermalization of subsystems, I was able to show that we can still use the predictions of statistical mechanics to describe the equilibrium of some observables. Moreover, the intuition developed in the process led me to propose an experimentally accessible way to unravel the interacting nature of many-body localised systems. Second, I exploited the "Concentration of Measure" phenomenon to study the macroscopic properties of the basis states of Loop Quantum Gravity. These techniques were previously used to explain why the thermal behaviour in quantum systems is such an ubiquitous phenomenon, at the macroscopic scale. I focused on the local properties, their thermodynamic behaviour and interplay with the semiclassical limit. This was motivated by the necessity to understand, from a quantum gravity perspective, how and why a classical horizon exhibits thermal properties.