## Random matrix theory of the isospectral twirling

Salvatore F. E. Oliviero, Lorenzo Leone, Francesco Caravelli, Alioscia Hamma

SciPost Phys. 10, 076 (2021) · published 25 March 2021

- doi: 10.21468/SciPostPhys.10.3.076
- Submissions/Reports

### 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.

### Cited by 13

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Salvatore Francesco Emanuele Oliviero, -
^{1}Lorenzo Leone, -
^{2}Francesco Caravelli, -
^{1}Alioscia Hamma