Random Matrix Theory of the Isospectral twirling

TL;DR

This paper introduces the concept of Isospectral twirling to analyze quantum dynamics, using random matrix theory to distinguish between chaotic and integrable systems through various quantum information measures.

Contribution

It systematically constructs probes for isospectral ensembles of Hamiltonians, expanding methods to analyze quantum chaos and integrability via spectral probability distributions.

Findings

Isospectral twirling effectively differentiates chaotic from integrable quantum systems.

Averages over ensembles reveal clear distinctions in quantum dynamical quantities.

The framework extends to various quantum processes, including quantum batteries and CP-maps.

Abstract

We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those defined by salient spectral probability distributions. The Gaussian Unitary Ensembles (GUE) describes a class of quantum chaotic Hamiltonians, while spectra corresponding to the Poisson and Gaussian Diagonal Ensemble (GDE) describe non chaotic, integrable dynamics. We compute the Isospectral twirling of several classes of important quantities in the analysis of quantum many-body systems: Frame potentials, Loschmidt Echos, OTOCs, Entanglement, Tripartite mutual information, coherence, distance to equilibrium states, work in quantum batteries and extension to CP-maps. Moreover, we perform averages in these ensembles by random matrix theory and show how these quantities clearly separate chaotic quantum dynamics from non chaotic ones.