量子场与Unruh-DeWitt探测器相互作用的热分布

中文摘要 AI 辅助

我们在Minkowski时空中引入了一个用于量子场与Unruh-DeWitt探测器之间热交换统计的操作性框架。利用干涉测量协议，我们在不进行投影测量的情况下定义了热的特征函数，并与相对论因果性保持一致。我们推导了该函数及热分布的微扰表达式。在真空中，统计结果与单向泊松定律的低强度展开一致，而对于Kubo-Martin-Schwinger（KMS）态，在微扰论二阶以内具有双向泊松结构。我们研究了涨落关系如何从探测器性质和场关联中涌现，并识别出它们退化为已知热交换涨落关系的区域。我们将熵Landauer不等式推导为Jakšić和Pillet代数熵平衡定理的特例，并在微扰探测器-场相互作用中对其进行了数值验证。我们将其紧致性与从热完全计数统计导出的互补Landauer界进行了比较，分析了它们对探测器初始态和相互作用时间的依赖性。我们还为显式开关的探测器-场动力学制定了第一和第二定律，识别出协调场能增益与探测器能量变化的外部开关功。在无间隙和δ开关区域，动力学允许非微扰处理，特征函数与双向泊松过程一致，从而产生由KMS条件确定的精确涨落定理。这些结果为相对论量子场论中的热统计提供了一致框架，并阐明了涨落关系的涌现。

英文摘要

We introduce an operational framework for heat-exchange statistics between a quantum field and an Unruh-DeWitt detector in Minkowski spacetime. Using an interferometric protocol, we define the characteristic function of heat without projective measurements, consistently with relativistic causality. We derive perturbative expressions for this function and the heat distribution. In the vacuum, the statistics coincides with the low-intensity expansion of a unidirectional Poisson law, while for Kubo-Martin-Schwinger (KMS) states it has a bidirectional Poisson structure up to second order in perturbation theory. We study how fluctuation relations emerge from detector properties and field correlations, identifying regimes where they reduce to known heat-exchange fluctuation relations. We derive the entropic Landauer inequality as a specialization of the algebraic entropy-balance theorem of Jakšić and Pillet and verify it numerically within the perturbative detector-field interaction. We compare its tightness with a complementary Landauer bound derived from the full counting statistics of heat, analyzing their dependence on the detector's initial state and interaction time. We also formulate the first and second laws for the explicitly switched detector-field dynamics, identifying the external switching work that reconciles the field-energy gain with the detector-energy change. In the gapless and delta-switching regimes, where the dynamics admits a non-perturbative treatment, the characteristic function coincides with that of a bidirectional Poisson process, yielding an exact fluctuation theorem determined by the KMS condition. These results provide a consistent framework for heat statistics in relativistic quantum field theory and clarify the emergence of fluctuation relations.

发表机构

• Universidade Estadual de Campinas（坎皮纳斯州立大学）

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