Surface state decoherence in loop quantum gravity, a first toy model

TL;DR

This paper introduces a toy model within loop quantum gravity to study how surface geometries decohere and recohere, shedding light on black hole horizon decoherence and the limitations of master equation approximations.

Contribution

It presents the first toy model for surface state decoherence in loop quantum gravity, analyzing dynamics and comparing exact evolution with Lindblad-type approximations.

Findings

Decoherence and recoherence phenomena observed in the toy model

Comparison highlights limitations of Lindblad master equations

Provides insights into boundary decoherence of black hole horizons

Abstract

The quantum-to-classical transition through decoherence is a major facet of the semi-classical analysis of quantum models that are supposed to admit a classical regime, as quantum gravity should be. A particular problem of interest is the decoherence of black hole horizons and holographic screens induced by the bulk-boundary coupling with interior degrees of freedom. Here in this paper we present a first toy-model, in the context of loop quantum gravity, for the dynamics of a surface geometry as an open quantum system at fixed total area. We discuss the resulting decoherence and recoherence and compare the exact density matrix evolution to the commonly used master equation approximation {\it \`a la} Lindblad underlining its merits and limitations. The prospect of this study is to have a clearer understanding of the boundary decoherence of black hole horizons seen by outside observers.