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

• URL: http://arxiv.org/abs/2603.18946v1
• Date: Thu, 19 Mar 2026 14:21:05 GMT
• Title: Dependence of Lindbladian spectral statistics on the integrability of no-jump Hamiltonians and the recycling terms
• Abstract summary: We show that recycling processes, symmetry constraints, and the Liouville-space structure crucially shape the spectral correlations.<n>Our work establishes a unified spectral-statistics characterization for Lindbladians and their associated effective non-Hermitian Hamiltonians.
• Score: 7.016643488761326
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 regular to chaotic. Our work establishes a unified spectral-statistics characterization for Lindbladians and their associated effective non-Hermitian Hamiltonians, deepening our understanding of integrable and chaotic spectral properties in open many-body systems.

Related papers

• When level repulsion fails: non-normality and chaos in open quantum systems [0.0]
  For Hamiltonian systems, level statistics provide a faithful diagnostic of quantum chaos.<n>We show that level statistics cannot universally serve as a reliable diagnostic of quantum chaos in open quantum systems.
  arXiv  Detail & Related papers  (2026-03-31T18:26:57Z)
• Spectral Decimation of Quantum Many-Body Hamiltonians [1.1327508153380308]
  We develop a theory of spectral decimation for quantum many-body Hamiltonians.<n>We show that it provides a quantitative probe of emergent symmetries in statistically mixed spectra.
  arXiv  Detail & Related papers  (2026-02-23T19:00:05Z)
• Statistical Signatures of Integrable and Non-Integrable Quantum Hamiltonians [1.1327508153380308]
  We develop a statistical framework that approaches quantum integrability from a probabilistic standpoint.<n>A key observation is that integrability requires a finite probability of vanishing energy gaps.<n>We propose a two-step protocol to distinguish integrable from non-integrable Hamiltonians.
  arXiv  Detail & Related papers  (2025-10-02T18:00:03Z)
• Evolution of multi-qubit correlations driven by mutual interactions [49.1574468325115]
  We analyze the evolution of the correlation tensor elements of quantum systems composed of $frac12$-spins.<n>We show how a strong external field can play a stabilizing factor with respect to certain correlation characteristics.
  arXiv  Detail & Related papers  (2025-07-01T11:45:08Z)
• Liouvillian and Hamiltonian exceptional points of atomic vapors: The spectral signatures of quantum jumps [0.0]
  We investigate spectral singularities in an alkali-metal atomic vapor modeled using four and effectively three hyperfine states.<n>By comparing the eigenvalue spectra of a non-Hermitian Hamiltonian (NHH) and a Liouvillian superoperator, we analyze the emergence and characteristics of both semiclassical and quantum exceptional points.
  arXiv  Detail & Related papers  (2025-06-03T14:08:27Z)
• Isospectrality and non-locality of generalized Dirac combs [41.94295877935867]
  We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions.<n>We classify a large class of isospectral relations, determining which Hamiltonians are spectrally unique, and which are instead related by a unitary or anti-unitary transformation.
  arXiv  Detail & Related papers  (2025-05-23T13:58:50Z)
• Avoided-crossings, degeneracies and Berry phases in the spectrum of quantum noise through analytic Bloch-Messiah decomposition [49.1574468325115]
  "analytic Bloch-Messiah decomposition" provides approach for characterizing dynamics of quantum optical systems.<n>We show that avoided crossings arise naturally when a single parameter is varied, leading to hypersensitivity of the singular vectors.<n>We highlight the possibility of programming the spectral response of photonic systems through the deliberate design of avoided crossings.
  arXiv  Detail & Related papers  (2025-04-29T13:14:15Z)
• From angular coefficients to quantum observables: a phenomenological appraisal in di-boson systems [44.99833362998488]
  Motivated by the growing interest in accessing the spin structure of multi-boson processes, we study polarisation and spin-correlation coefficients in di-boson systems. We show that higher-order corrections of QCD and electroweak type, off-shell modelling, and realistic effects such as fiducial selections and neutrino reconstruction are unavoidable.
  arXiv  Detail & Related papers  (2024-09-25T08:30:54Z)
• Quantum space-time Poincaré inequality for Lindblad dynamics [15.031583573428481]
  We show that incorporating a Hamiltonian component into a detailed balanced Lindbladian can generically enhance its spectral gap.<n>We derive explicit and constructive exponential decay estimates for convergence in the noncommutative $L2$-norm.<n>This analysis relies on establishing a quantum analog of space-time Poincar'e inequality.
  arXiv  Detail & Related papers  (2024-06-13T13:43:41Z)
• Sufficient condition for gapless spin-boson Lindbladians, and its connection to dissipative time-crystals [64.76138964691705]
  We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems. We argue that gapless modes can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals.
  arXiv  Detail & Related papers  (2022-09-26T18:34:59Z)
• Quantum particle across Grushin singularity [77.34726150561087]
  We study the phenomenon of transmission across the singularity that separates the two half-cylinders. All the local realisations of the free (Laplace-Beltrami) quantum Hamiltonian are examined as non-equivalent protocols of transmission/reflection. This allows to comprehend the distinguished status of the so-called bridging' transmission protocol previously identified in the literature.
  arXiv  Detail & Related papers  (2020-11-27T12:53:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.