Qubit heating near a hotspot

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 ref. [23] 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 phi 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 phi-hotspot coupling. We compute the thermalization time, and find that it varies inversely with the phi-qubit coupling strength in the standard way.

Automated summary

The study investigates the interaction between Unruh-DeWitt detectors and a massless quantum field phi coupled to a hotspot, identifying a Markovian regime where thermalization occurs depending on the proximity of the qubit to the hotspot. The thermalization time is found to vary inversely with the phi-qubit coupling strength in a standard manner.