arXiv 2007.059842020-07hep-thgr-qc

地平线上的量子比特：黑洞附近的退相干和热化

Qubits on the Horizon: Decoherence and Thermalization near Black Holes

Greg Kaplanek, C. P. Burgess

备注：: 24 pages plus appendix, 2 figures v2) now published in JHEP, typos fixed and added subsection on the frame independence of the Markovian limit
发表信息：: JHEP 01 (2021) 098
DOI：: 10.1007/JHEP01(2021)098

摘要：

我们研究了一个量子比特（或Unruh-De Witt探测器）的后期演化，它徘徊在史瓦西黑洞的事件视界附近，同时与自由量子标量场相互作用。计算是在无量纲量子位/场耦合$g$中微扰进行的，但不是计算由于场相互作用引起的量子位激发率（如通常所做的那样），而是使用开放EFT技术来计算$g^2 t/r_s$中所有阶次的后期演化（同时忽略阶次$g^4 t/r_s$效应），其中$r_s = 2GM$是史瓦西半径。我们证明了，对于足够接近视界的量子比特，晚期演化采取一种简单的普遍形式，只依赖于近视界几何，假设量子场是在阿达玛型状态（如Hartle-Hawking或Unruh真空）中制备的。当两个量子比特态之间的红移能量差$ω_\infty$（由远处的观察者观察探测器测量）满足$ω_\infty r_s \ll 1$时，这种普适演化变成马尔可夫，并描述了与霍金辐射平衡的指数方法，量子比特密度矩阵的非对角和对角分量以不同的特征时间松弛到平衡，都是$r_s/g^2$阶。

英文摘要：

We examine the late-time evolution of a qubit (or Unruh-De Witt detector) that hovers very near to the event horizon of a Schwarzschild black hole, while interacting with a free quantum scalar field. The calculation is carried out perturbatively in the dimensionless qubit/field coupling $g$, but rather than computing the qubit excitation rate due to field interactions (as is often done), we instead use Open EFT techniques to compute the late-time evolution to all orders in $g^2 t/r_s$ (while neglecting order $g^4 t/r_s$ effects) where $r_s = 2GM$ is the Schwarzschild radius. We show that for qubits sufficiently close to the horizon the late-time evolution takes a simple universal form that depends only on the near-horizon geometry, assuming only that the quantum field is prepared in a Hadamard-type state (such as the Hartle-Hawking or Unruh vacua). When the redshifted energy difference, $ω_\infty$, between the two qubit states (as measured by a distant observer looking at the detector) satisfies $ω_\infty r_s \ll 1$ this universal evolution becomes Markovian and describes an exponential approach to equilibrium with the Hawking radiation, with the off-diagonal and diagonal components of the qubit density matrix relaxing to equilibrium with different characteristic times, both of order $r_s/g^2$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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英文摘要：

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