Trace-class spectra of irreducible Gaussian quantum Markov semigroups

• URL: http://arxiv.org/abs/2609.06957v1
• Date: Mon, 07 Sep 2026 02:53:41 GMT
• Title: Trace-class spectra of irreducible Gaussian quantum Markov semigroups
• Abstract summary: For stable drift, irreducibility is equivalent to the existence of a unique faithful normal invariant state.<n>For periodic critical drift, we obtain an explicit spectral formula that includes the displacement and yields horizontal half-lines or parabolic regions.
• Score: 4.519380970399272
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We determine the spectrum of the predual generator of an irreducible Gaussian quantum Markov semigroup on the trace-class operators over a finite-mode bosonic Fock space in the stable, strictly unstable, and periodic critical drift regimes. For stable drift, irreducibility is equivalent to the existence of a unique faithful normal invariant state. The spectrum and approximate point spectrum are the closed left half-plane, whereas the point spectrum is the open left half-plane together with zero. Thus the polynomial eigenvalues generated by the drift matrix do not exhaust the trace-class point spectrum. If the drift has an eigenvalue with strictly positive real part, the spectrum is again the closed left half-plane, but the point spectrum is empty and the open left half-plane together with zero belongs to the residual spectrum. For periodic critical drift, we obtain an explicit spectral formula that includes the displacement parameter and yields horizontal half-lines or parabolic regions. The proofs use characteristic functions, Gaussian diffusion semigroups, and bounded eigenoperators of the dual semigroup. The nonperiodic critical drift case remains open.

Related papers

• Entanglement, anti-flatness, and nonlocal nonstabilizerness: a unified perspective from entanglement spectrum [3.6661773891142744]
  Entanglement and nonstabilizerness capture distinct aspects of quantum complexity, yet their relation through the entanglement spectrum remains only partially understood.<n>Here we develop a unified spectral framework for bipartite nonlocal nonstabilizerness.<n>Our spectral bounds and dyadic-shell sandwich construction provide general tools for analyzing nonlocal SRE, offering a flexible framework that can be applied to a wide range of entanglement spectra in quantum many-body systems.
  arXiv  Detail & Related papers  (2026-09-02T02:00:20Z)
• Quantum Chaos with a Macroscopic Zero-Mode Sector [36.947315248138345]
  Chaotic many-body spectra are expected to densely fill their energy window.<n>We show that constrained spin chains with chiral symmetry evade this expectation by hosting an exponentially large manifold of symmetry-protected exact zero modes.
  arXiv  Detail & Related papers  (2026-07-10T15:17:05Z)
• Entanglement-spectrum fingerprint of a non-invertible symmetry: the Kramers--Wannier duality defect on the lattice [11.171049368197778]
  Non-invertible symmetries are characterized by topological defects of irrational quantum dimension.<n>We show that the categorical data of the canonical example -- the Kramers--Wannier (KW) duality defect of the critical Ising chain -- is encoded in the single-particle entanglement spectrum of its ground state.
  arXiv  Detail & Related papers  (2026-07-01T16:21:58Z)
• Unitary Time Evolution and Vacuum for a Quantum Stable Ghost [36.94429692322632]
  We prove that due to an integral of motion with a positive discrete spectrum the Hamiltonian has a pure point spectrum unbounded in both directions.<n>We argue that the discrete spectrum of the integral of motion enforces stability for extended interactions.
  arXiv  Detail & Related papers  (2026-04-23T16:15:51Z)
• Bound, antibound and resonance two-photon states in chiral waveguide QED [51.56484100374058]
  We present a theoretical study of the two-particle spectrum $(K)$ for the chiral waveguide QED setup.<n>For each pair center-of-mass momentum $K$ there exist distinct solutions with $Imle 0$ in the two-particle spectrum.<n>An interesting finding is that the real part of the spectrum $Re (K)$ in the chiral model is gapless.
  arXiv  Detail & Related papers  (2026-04-22T14:19:46Z)
• Typical entanglement in anyon chains: Page curves beyond Lie group symmetries [41.99844472131922]
  We study bipartite entanglement statistics in one-dimensional anyon chains constrained by fusion rules of unitary pre-modular categories.<n>Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(sqrtL)$ or $O(1)$ symmetry-type corrections.<n> Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions.
  arXiv  Detail & Related papers  (2026-03-26T18:00:03Z)
• Universality of equilibration dynamics after quantum quenches [0.0]
  We show that in an appropriate scaling limit the lower part of the entanglement spectrum exhibits universality''<n>We benchmark our analytical results in free-fermion chains, such as the transverse field Ising chain and the XX chain, in the rule 54 chain, and in Bethe ansatz solvable spin models.
  arXiv  Detail & Related papers  (2025-12-24T18:19:57Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Tackling Combinatorial Distribution Shift: A Matrix Completion Perspective [42.85196869759168]
  We study a setting we call distribution shift, where (a) under the test- and training-random data, the labels $z$ are determined by pairs of features $(x,y)$, (b) the training distribution has coverage of certain marginal distributions over $x$ and $y$ separately, but (c) the test distribution involves examples from a product distribution over $(x,y)$ that is not covered by the training distribution.
  arXiv  Detail & Related papers  (2023-07-12T21:17:47Z)
• Fundamental transfer matrix for electromagnetic waves, scattering by a planar collection of point scatterers, and anti-PT-symmetry [0.0]
  We develop a fundamental transfer-matrix formulation of the scattering of electromagnetic waves. We show that identical and $mathcalPmathcalT$-symmetric doublets do not admit spectral singularities. We also show that a generic anti-$mathcalPmathcalT$-symmetric doublet possesses a continuous lasing spectrum.
  arXiv  Detail & Related papers  (2022-12-06T18:23:52Z)
• Spectra of generators of Markovian evolution in the thermodynamic limit: From non-Hermitian to full evolution via tridiagonal Laurent matrices [0.0]
  generators of single-particle, translation-invariant Lindblad operators on the infinite line are unitarily equivalent to direct integrals of finite-range bi-infinite Laurent operator with finite-range perturbations.
  arXiv  Detail & Related papers  (2022-06-20T16:32:14Z)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)
• 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.