Dependence of Lindbladian spectral statistics on the integrability of no-jump Hamiltonians and the recycling terms

TL;DR

This paper investigates how the spectral statistics of Lindbladians depend on the integrability of no-jump Hamiltonians and recycling terms, revealing conditions for Poisson and Ginibre statistics in open quantum systems.

Contribution

It provides a unified spectral-statistics framework for Lindbladians and their effective Hamiltonians, highlighting the influence of recycling, symmetry, and structure on spectral correlations.

Findings

Recycling processes and symmetry constraints shape spectral correlations.

Identified Lindbladians with Poisson spectral statistics despite varying effective Hamiltonian statistics.

Established a unified spectral-characterization for Lindbladians and non-Hermitian Hamiltonians.

Abstract

Spectral statistics probe integrability versus chaos and have recently been extended to Markovian open quantum systems described by Lindbladians, whose quantum-trajectory unraveling decomposes the evolution into no-jump dynamics generated by an effective non-Hermitian Hamiltonian and recycling jumps. In this work, we perform spectrum-statistics diagnostics for Lindbladians and their effective non-Hermitian Hamiltonians. We show that recycling processes, symmetry constraints, and the Liouville-space structure crucially shape the spectral correlations. In particular, we identify a family of spectrally separable Lindbladians whose spectra exhibit robust Poisson statistics, despite the effective non-Hermitian Hamiltonian varying from Poisson to Ginibre statistics. Our work establishes a unified spectral-statistics characterization for Lindbladians and their associated effective non-Hermitian Hamiltonians, deepening our understanding of spectral properties in open many-body systems.