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

Understand

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.