Equilibration in low-dimensional quantum matrix models

Abstract

Matrix models play an important role in studies of quantum gravity, being candidates for a formulation of M-theory, but are notoriously difficult to solve. In this work, we present a fresh approach by introducing a novel exact model provably equivalent with low-dimensional bosonic matrix models. In this equivalent model significant local structure becomes apparent and it can serve as a simple toy model for analytical and precise numerical study. We derive a substantial part of the low energy spectrum, find a conserved charge, and are able to derive numerically the Regge trajectories. To exemplify the usefulness of the approach, we address questions of equilibration starting from a non-equilibrium situation, building upon an intuition from quantum information. We finally discuss possible generalizations of the approach.

5+2 pages, 2 figures; v2: published version

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• The smallest matrix black hole model in the classical limit
• The quantum cat map on the modular discretization of extremal black hole horizons
• Matrix Thermalization
• Chaos in $SU(2)$ Yang-Mills Chern-Simons Matrix Model
• Chaos from Equivariant Fields on Fuzzy $S^4$
• Fast Scramblers, Democratic Walks and Information Fields