Random matrix theory and Hawking radiation

In 1973, Stephen Hawking predicted that black holes radiate at a temperature inversely proportional to their mass. This causes the black hole to lose mass and evaporate. While simple models of the evaporation process may break unitarity by evolving an initially pure state into a mixed state, there exist various models and scenarios that restore unitarity by introducing correlations between different radiation modes, so that the final state is pure. In this talk, I will take an agnostic view with respect to the precise mechanism of restoring unitarity and just ask the question what we can learn about the final state if we only assume (a) that the final state is pure and (b) that it is approximately Gaussian. Using tools from random matrix theory, I will construct the explicit ensemble of all pure Gaussian states that resembles mode-by-mode the thermal radiation predicted by Hawking and show that the required entanglement between individual modes is generally vanishingly small. I will discuss these findings in the context of studying the thermalization of isolated quantum systems. [based on Phys. Rev. Lett. 133, 060202 (2024), arXiv:2311.10562]