Thermalization in massive deformations of Yang-Mills matrix models

TL;DR

This study numerically investigates how a massive deformation of the Yang-Mills matrix model thermalizes over time, revealing dependencies on matrix size and energy, and proposing an estimation method for thermalization time.

Contribution

It introduces a numerical analysis of thermalization in a massive Yang-Mills matrix model with new insights into thermalization timescales and their dependence on model parameters.

Findings

Thermalization occurs from specific initial conditions.

Thermalization time scales logarithmically with matrix size.

Thermalization time varies with energy levels.

Abstract

We numerically study the classical evolution of a Yang-Mills matrix model with two distinct mass deformation terms, which can be contemplated as a massive deformation of the bosonic part of the BFSS model. Through numerical analysis, it is shown that when the simulations are started from a certain set of initial conditions, thermalization occurs. Besides, an estimation method is proposed to determine the approximate thermalization time. Using this method, we demonstrate that thermalization time vary logarithmically with increasing matrix size when the mass terms differ. Introducing a matrix configuration, we also obtain reduced actions and subsequently analyze how the thermalization time change as a function of the energy.