Quantum Chaos in Multi-Matrix Models

TL;DR

This paper investigates how interactions in multi-matrix quantum models affect the expected semicircular law of energy level densities, providing insights into deviations observed in complex quantum systems.

Contribution

It introduces a detailed analysis of multi-matrix models showing how interactions modify the spectral density, connecting quantum chaos with matrix model behavior.

Findings

Interactions alter the semicircular law in 2-matrix models

Different interaction types are explored in chain- and star-multimatrix models

Connections with Calogero-Sutherland models are discussed

Abstract

We propose a possible resolution for the problem of why the semicircular law is not observed, whilst the random matrix hypothesis describes well the fluctuation of energy spectra. We show in the random 2-matrix model that the interactions between the quantum subsystems alter the semicircular law of level density. We consider also other types of interactions in the chain- and star-multimatrix models. The connection with the Calogero-Sutherland models is briefly discussed.