Black holes as random particles: entanglement dynamics in infinite range and matrix models

TL;DR

The paper develops a unitary, all-to-all coupled (democratic) quantum model with GOE random couplings as a tractable surrogate for black hole dynamics. It analytically tracks time evolution of two-point correlators and entanglement entropies for out-of-equilibrium states, showing fast global thermalization with entanglement determined by occupation densities and factorization of reduced density matrices. The insights are extended to large-N matrix models via gauge-invariant generalized free-field entanglement, where entanglement is governed by quasinormal frequencies and three time scales emerge. The results challenge the fast scrambling conjecture, propose a dynamical picture for the brick-wall horizon, and illuminate how thermodynamic limits render a non-unitary effective evolution in democratic systems.

Abstract

We first propose and study a quantum toy model of black hole dynamics. The model is unitary, displays quantum thermalization, and the Hamiltonian couples every oscillator with every other, a feature intended to emulate the color sector physics of large-$\mathcal{N}$ matrix models. Considering out of equilibrium initial states, we analytically compute the time evolution of every correlator of the theory and of the entanglement entropies, allowing a proper discussion of global thermalization/scrambling of information through the entire system. Microscopic non-locality causes factorization of reduced density matrices, and entanglement just depends on the time evolution of occupation densities. In the second part of the article, we show how the gained intuition extends to large-$\mathcal{N}$ matrix models, where we provide a gauge invariant entanglement entropy for `generalized free fields', again depending solely on the quasinormal frequencies. The results challenge the fast scrambling conjecture and point to a natural scenario for the emergence of the so-called brick wall or stretched horizon. Finally, peculiarities of these models in regards to the thermodynamic limit and the information paradox are highlighted.