Quantum Lyapunov exponents and complex spacing ratios: Two measures of dissipative quantum chaos

Abstract

The agenda of dissipative quantum chaos is to create a toolbox that would allow us to categorize open quantum systems into “chaotic” and “regular” ones. Two approaches to this categorization have been proposed recently. One of them is based on the spectral properties of generators of open quantum evolution. The other one utilizes the concept of Lyapunov exponents to analyze quantum trajectories obtained by unraveling this evolution. By using two quantum models, we relate the two approaches and try to understand whether there is an agreement between the corresponding categorizations. Our answer is affirmative.

Spectral Properties of Disordered Interacting Non-Hermitian Systems

“…Because of the growing interest in non-hermitian physics, some of these properties have been generalized for non-hermitian Hamiltonians with complex eigenvalues to understand chaos or lack thereof 61,65,66 . Specifically, level spacing statistics and generalized complex spacing ratio have been calculated for open systems with the Lindbladian approach [67][68][69][70] , non-hermitian interacting disordered 61,[71][72][73] and quasiperiodic 62 systems. The complex spacing ratio has also been calculated for non-hermitian Dirac operators 74 , dissipative quantum circuits 75 , and noninteracting, non-hermitian disordered models in higher dimensions 76,77 .…”

Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model

“…Unfolding problems have been ameliorated in the last years for short-range observables with the introduction of spectral observables such as the adjacent gap ratios [15] for complex spectra [16] that do not require unfolding. They have already been applied in a variety of non-Hermitian systems: phase transitions in many-body Liouvillians [17][18][19][20], non-Hermitian…”