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arXiv · 2603.18946

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

Dingzu Wang·Hao Zhu·Guo-Feng Zhang·Dario Poletti
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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.

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Dingzu Wang, Hao Zhu, Guo-Feng Zhang, Dario Poletti. 2026-03-19. Dependence of Lindbladian spectral statistics on the integrability of no-jump Hamiltonians and the recycling terms. https://arxiv.org/abs/2603.18946

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