加速探测器对普朗克尺度变化敏感吗？
Are accelerated detectors sensitive to Planck scale changes?
AI总结：
本研究通过Unruh-DeWitt探测器探测Rindler视界位移，发现有限时间响应可区分宏观与微观位移，提供识别普朗克尺度效应的操作方案。
摘要：
量子引力分析中最首要的关切之一，是经典视界的位置在完整的量子分析下是否保持稳定。原则上，任何经典描述在插值到微观层面时，都可能变得易于发生涨落。在这种情况下，一个令人好奇的问题是：如果确实存在普朗克尺度上的此类涨落，它们对于远离普朗克尺度发生的物理过程是否具有任何意义？在本工作中，我们探讨小尺度的问题，并研究视界结构中是否存在普朗克尺度位移的明确特征。在近期的一项工作（arXiv:2107.03406）中，有人提出，在一系列嵌套的Rindler因果楔中，先前Rindler框架的真空对于移动后的Rindler框架而言表现为热布居。Bogoliubov分析依赖于量子场论的全局概念，结果证明对视界位移的局域特征不敏感。我们通过Unruh-DeWitt探测器研究该系统，探究这一量子场论的局域探针是否对位移参数足够敏感，从而揭示任何微观效应。对于无限时间响应的情况，我们恢复了热谱，从而再次确认无限时间响应探测的是场的全局性质。另一方面，有限时间响应被发现以一种特殊方式对位移参数敏感：任何具有能量间隙$Ωc/a \sim 1$且在时间尺度$T a/c \sim 1$内运行的探测器，对于视界的宏观和微观位移，其响应存在可测量的差异，这为我们提供了直接探测Rindler楔之间最微小间隔的手段。因此，本研究提供了一种可操作的方法来识别普朗克尺度效应，并可推广到其他各种有趣的引力设置中。
英文摘要：
One of the foremost concerns in the analysis of quantum gravity is whether the locations of classical horizons are stable under a full quantum analysis. In principle, any classical description, when interpolated to the microscopic level, can become prone to fluctuations. The curious question in that case is if there indeed are such fluctuations at the Planck scale, do they have any significance for physics taking place at scales much away from the Planck scale? In this work, we address the question of small scales and address whether there are definitive signatures of Planck scale shifts in the horizon structure. In a recent work (arXiv:2107.03406), it was suggested that in a nested sequence of Rindler causal wedges, the vacua of preceding Rindler frames appear thermally populated to a shifted Rindler frame. The Bogoliubov analysis relies on the global notion of the quantum field theory and turns out to be insensitive to the local character of these horizon shifts. We investigate this system by means of the Unruh-DeWitt detector and see if this local probe of the quantum field theory is sensitive enough to the shift parameters to reveal any microscopic effects. For the case of infinite-time response, we recover the thermal spectrum, thus reaffirming that the infinite-time response probes the global properties of the field. On the other hand, the finite-time response turns out to be sensitive to the shift parameter in a peculiar way that any detector with energy gap $Ωc/a \sim 1$ and is operational for timescale $T a/c \sim 1$ has a measurably different response for a macroscopic and microscopic shift of the horizon, giving us a direct probe to the tiniest separation between the Rindler wedges. Thus, this study provides an operational method to identify Planck scale effects that can be generalized to various other interesting gravitational settings.
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