Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models

TL;DR

This paper investigates how non-Gaussian potentials and noise in random matrix models affect spectral properties, quantum chaos indicators, and complexity measures, revealing sensitivities to non-Gaussianity and decoherence effects.

Contribution

It introduces analysis of spectral form factor and Krylov complexity in non-Gaussian and noisy RMT models, highlighting their distinct behaviors and implications for open quantum systems.

Findings

Spectral form factor is suppressed at short times due to decoherence.

Krylov complexity deviates from Gaussian RMT in non-Gaussian and noisy models.

Long-time behaviors differ significantly between models.

Abstract

We study the spectral properties of two classes of random matrix models: non-Gaussian RMT with quartic and sextic potentials, and RMT with Gaussian noise. We compute and analyze the quantum Krylov complexity and the spectral form factor for both of these models. We find that both models show suppression of the spectral form factor at short times due to decoherence effects, but they differ in their long-time behavior. In particular, we show that the Krylov complexity for the non-Gaussian RMT and RMT with noise deviates from that of a Gaussian RMT. We discuss the implications and limitations of our results for quantum chaos and quantum information in open quantum systems. Our study reveals the distinct sensitivities of the spectral form factor and complexity to non-Gaussianity and noise, which contribute to the observed differences in the different time domains.