Nonequilibrium Phase Transitions in Large $N$ Matrix Quantum Mechanics

TL;DR

This paper explores nonequilibrium phase transitions in large N matrix quantum mechanics, revealing conditions for steady states and drawing parallels with quantum optics phenomena, using bootstrap methods for rigorous analysis.

Contribution

It introduces a study of nonequilibrium phase transitions in large N matrix quantum mechanics, including new classes of steady states and phase transition evidence, with bootstrap techniques for analysis.

Findings

Existence of steady states in unbounded potentials with strong dissipation.

Evidence of nonequilibrium phase transitions similar to quantum optics systems.

Preliminary results on two-matrix quantum mechanics.

Abstract

It is believed that the theory of quantum gravity describing our universe is unitary. Nonetheless, if we only have access to a subsystem, its dynamics is described by nonequilibrium physics. Motivated by this, we investigate the planar limit of large $N$ ungauged one-matrix quantum mechanics obeying the Lindblad master equation with dissipative jump terms, focusing on the existence, uniqueness, and properties of steady states that signal nonequilibrium phase transitions. In the first class of examples, where potentials are unbounded from below, we study nonequilibrium critical points above which strong dissipation allows for the existence of normalizable steady states that would otherwise not exist. In the second class of examples, termed matrix quantum optics, we find evidence of nonequilibrium phase transitions analogous to those recently reported in the quantum optics literature for driven-dissipative Kerr resonators. Preliminary results on two-matrix quantum mechanics are also presented. We implement bootstrap methods to obtain concrete and rigorous results for the nonequilibrium steady states of matrix quantum mechanics in the planar limit.