Quantum Hotspots: Mean Fields, Open EFTs, Nonlocality and Decoherence Near Black Holes

Abstract

Effective theories describing black hole exteriors resemble open quantum systems inasmuch as many unmeasurable degrees of freedom beyond the horizon interact with those we can see. A solvable Caldeira-Leggett type model of a quantum field that mixes with many unmeasured thermal degrees of freedom on a shared surface was proposed in arXiv:2106.09854 to provide a benchmark against which more complete black hole calculations might be compared. We here use this model to test two types of field-theoretic approximation schemes that also lend themselves to describing black hole behaviour: Open EFT techniques (as applied to the fields themselves, rather than Unruh-DeWitt detectors) and mean-field methods. Mean-field methods are of interest because the effective Hamiltonians to which they lead can be nonlocal; a possible source for the nonlocality that is sometimes entertained as being possible for black holes in the near-horizon regime. Open EFTs compute the evolution of the field state, allowing discussion of thermalization and decoherence even when these occur at such late times that perturbative methods fail (as they often do). Applying both of these methods to a solvable system identifies their domains of validity and shows how their predictions relate to more garden-variety perturbative tools.

Qubit Heating Near a Hotspot

“…It was with the view to providing one of these benchmarks that reference [17] proposed a solvable Caldeira-Leggett style [18,19] model consisting of an external massless quantum field φ interacting with many unseen gapless thermal fields in a very small spatial volume (called a 'hotspot'). Some implications of this model, such as for the coherence of the state of the field φ, are explored in a companion paper [20].…”

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

“…There are several directions in which this model might fruitfully be explored. In a companion work [43], we apply to it several approximate Open-EFT techniques designed to probe late-time evolution, to better identify their domains of validity and whether they can illuminate the extent to which the open nature of the hotspot causes a breakdown of local descriptions of the physics of the field φ living in R + . A second companion [44] explores the behaviour of an Unruh detector (or qubit) that couples to the field φ in the vicinity of the hotspot, to determine the extent to which it thermalizes as a function of its couplings and its distance from the hotspot.…”

“…Note however that the full correlation function W β = S + E β is not explicitly thermal since the temperature-independent contribution S obviously fails to satisfy a KMS-like condition analogous to (D.63). However, in a limit where E β dominates over S (provided t > |x| and t > |x |) one should expect to see thermality manifest itself more directly (this is explored using an Unruh-Dewitt detector model in [43], where it is shown that a stationary qubit outside the hotspot thermalizes whilst only interacting with φ).…”

“…Although the extra degrees of freedom can again be integrated out, they are not the traditional massive states of the usual Wilsonian treatments, and so can lead to actions with unusual properties including some forms of nonlocality. In companion papers [43,44] we use the hotspot model to explore some of these properties in an effort to ascertain the rules for such an EFT, and the extent to which locality and ordinary Wilsonian reasoning breaks down.…”

“…The remainder of this paper sets up the hotspot framework and derives the equations that govern how φ responds to the hotspot (topics that dominate the discussion of §2). Along the way we also make some preliminary explorations of its physical implications (with more to follow in [43,44]). We find in particular the following noteworthy properties.…”