Spectral Form Factor for Time-dependent Matrix model

TL;DR

This paper investigates the spectral form factor in a time-dependent Gaussian random matrix model, revealing a rounded dip-ramp-plateau behavior and comparing numerical and analytical results for finite and large matrix sizes.

Contribution

It introduces a time-dependent matrix model and analyzes its spectral form factor, highlighting differences from the standard model and providing both numerical and analytical insights.

Findings

Spectral form factor exhibits rounded dip-ramp-plateau behavior.

Analytic large N expressions match numerical finite N evaluations.

Model extends understanding of quantum chaos in time-dependent systems.

Abstract

The quantum chaos is related to a Gaussian random matrix model, which shows a dip-ramp-plateau behavior in the spectral form factor for the large size $N$. The spectral form factor of time dependent Gaussian random matrix model shows also dip-ramp-plateau behavior with a rounding behavior instead of a kink near Heisenberg time. This model is converted to two matrix model, made of $M_1$ and $M_2$. The numerical evaluation for finite $N$ and analytic expression in the large $N$ are compared for the spectral form factor.