Qubit Heating Near a Hotspot

Abstract

Effective theories describing black hole exteriors contain many open-system features due to the large number of gapless degrees of freedom that lie beyond reach across the horizon. A simple solvable Caldeira-Leggett type model of a quantum field interacting within a small area with many unmeasured thermal degrees of freedom was recently proposed in arXiv:2106.09854 to provide a toy model of this kind of dynamics against which more complete black hole calculations might be compared. We here compute the response of a simple Unruh-DeWitt detector (or qubit) interacting with a massless quantum field $\varphi$ coupled to such a hotspot. Our treatment differs from traditional treatments of Unruh-DeWitt detectors by using Open-EFT tools to reliably calculate the qubit's late-time behaviour. We use these tools to determine the efficiency with which the qubit thermalizes as a function of its proximity to the hotspot. We identify a Markovian regime in which thermalization does occur, though only for qubits closer to the hotspot than a characteristic distance scale set by the $\varphi$-hotspot coupling. We compute the thermalization time, and find that it varies inversely with the $\varphi$-qubit coupling strength in the standard way.

16 pages + appendices, 1 figure v2) now published in JHEP, typos fixed

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Cited by in corpus (1)

• Influence Through Mixing: Hotspots as Benchmarks for Basic Black-Hole Behaviour