AI 中文总结
本文针对量子系统大偏差理论的发展缺口，从量子游走到随机暴胀，分析了耦合热库的非简谐振子涨落、提出使测量诱导相对熵最小化的方法，并将其应用于宇宙学随机暴胀场景，揭示了德西特背景下长波长场密度矩阵的演化特性。
AI 中文摘要
物理系统中的稀有涨落取决于导致该涨落的详细微观物理机制。在经典统计系统中，大偏差原理已阐明了半经典理论在描述该区域的作用，同时为统计力学提供了数学基础。而量子系统的大偏差理论发展则滞后得多。由于所有物理系统本质上都是量子力学的，这导致我们对统计物理、宇宙学及其他领域相关的稀有涨落的理解存在重大缺口。本文中，我们发展了与计算从量子游走到宇宙学的物理系统中稀有事件相关的大偏差理论的实用方面。我们首先分析了耦合到热库的非简谐振子的情况，明确展示了系统如何从以统计（如热）涨落为主的状态演变为量子涨落为主的状态。随后，我们将这些结果进行推广，证明主导的稀有涨落使测量诱导的相对熵最小化。这一视角为广泛的开放量子系统提供了热力学描述。我们将这些结果应用于通过随机暴胀在宇宙学中产生的随机游走，证明固定德西特背景下长波长场的密度矩阵演化会破坏KMS对称性，从而产生不满足细致平衡的定态密度矩阵。
英文摘要
Rare fluctuations in physical systems depend on the detailed microphysics responsible for the fluctuations. In classical statistical systems, the large deviation principle has elucidated the role of semi-classics in describing this regime, and has simultaneously provided a the mathematical foundation of statistical mechanics. Large deviation theory for quantum system is considerably less developed. As all physical systems are fundamentally quantum mechanical, this leaves a major gap in our understanding of rare fluctuations relevant to statistical physics, cosmology, and more. In this paper, we develop the practical aspects of the theory of large deviations relevant for calculating rare events in physical systems from quantum walks to cosmology. We first analyze the case of the anharmonic oscillator coupled to a bath, showing explicitly how the system evolves from dominantly statistical (e.g. thermal) to quantum fluctuations. We then generalize these results, showing that the dominant rare fluctuations minimize the measurement-induced relative entropy. This perspective provides a thermodynamic description of a wide range of open quantum systems. We apply these results to random walks that arise in cosmology through stochastic inflation. We show that the evolution of the density matrix of long wavelength fields on a fixed de Sitter background breaks the KMS symmetry, giving rise to a stationary density matrix that does not respect detailed balance.
Comments65 pages, 5 figures
