Large N classical dynamics of holographic matrix models

TL;DR

This paper uses numerical simulations of classical matrix models related to M-theory to explore thermalization, chaos, and hydrodynamics at large N, providing insights into black hole duals in string theory.

Contribution

It introduces a detailed numerical approach to study classical dynamics of holographic matrix models and demonstrates evidence of thermalization, chaos, and hydrodynamic behavior at large N.

Findings

Evidence of thermalization through eigenvalue distributions.

Observation of chaotic dynamics and hydrodynamic limits.

Insights into black hole duals in string and M-theory.

Abstract

Using a numerical simulation of the classical dynamics of the plane-wave and flat space matrix models of M-theory, we study the thermalization, equilibrium thermodynamics and fluctuations of these models as we vary the temperature and the size of the matrices, N. We present our numerical implementation in detail and several checks of its precision and consistency. We show evidence for thermalization by matching the time-averaged distributions of the matrix eigenvalues to the distributions of the appropriate Traceless Gaussian Unitary Ensemble of random matrices. We study the autocorrelations and power spectra for various fluctuating observables and observe evidence of the expected chaotic dynamics as well as a hydrodynamic type limit at large N, including near-equilibrium dissipation processes. These configurations are holographically dual to black holes in the dual string theory or M-theory and we discuss how our results could be related to the corresponding supergravity black hole solutions.