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

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.