Horizon in Random Matrix Theory, Hawking Radiation and Flow of Cold Atoms

TL;DR

This paper establishes a novel connection between random matrix ensembles, black-hole physics, and cold atom systems, proposing a model that incorporates Hawking radiation effects in a 2D curved spacetime framework.

Contribution

It introduces a Gaussian scalar field theory in curved 2D space with an event horizon as an effective model for invariant random matrix ensembles, linking quantum chaos, gravity analogues, and cold atom experiments.

Findings

Hawking radiation emerges naturally in the RME model.

The model maps to gravitational analogues and BEC systems.

Potential for experimental realization in cold atom setups.

Abstract

We propose a Gaussian scalar field theory in a curved 2D metric with an event horizon as the low-energy effective theory for a weakly confined, invariant Random Matrix ensemble (RME). The presence of an event horizon naturally generates a bath of Hawking radiation, which introduces a finite temperature in the model in a non-trivial way. A similar mapping with a gravitational analogue model has been constructed for a Bose-Einstein condensate (BEC) pushed to flow at a velocity higher than its speed of sound, with Hawking radiation as sound waves propagating over the cold atoms. Our work suggests a three-fold connection between a moving BEC system, black-hole physics and unconventional RMEs with possible experimental applications.