Isospectrality and non-locality of generalized Dirac combs

• URL: http://arxiv.org/abs/2505.17920v1
• Date: Fri, 23 May 2025 13:58:50 GMT
• Title: Isospectrality and non-locality of generalized Dirac combs
• Authors: Giuliano Angelone, Manuel Asorey, Fernando Ezquerro, Paolo Facchi,
• Abstract summary: 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.
• Score: 41.94295877935867
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a generalization of Dirac's comb model, describing a non-relativistic particle moving in a periodic array of generalized point interactions. The latter represent the most general point interactions rendering the kinetic-energy operator self-adjoint, and form a four-parameters family that includes the $\delta$-potential and the $\delta'$-potential as particular cases. We study the parameter dependence of the spectral properties of this system, finding a rich isospectrality structure. We systematically 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.

Related papers

• 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)
• Universal Relation between Spectral and Wavefunction Properties at Criticality [0.0]
  Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization.<n>We conjecture that it represents a universal property of a broad class of critical models.<n>We derive a universal function $D_1(r)$, where $r$ is the averaged level spacing ratio.
  arXiv  Detail & Related papers  (2025-06-13T11:11:47Z)
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation.<n>We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue.<n>We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos [44.99833362998488]
  We develop an analytical approach to the spectral form factor and out-of-time ordered correlators in zero-dimensional Brownian models of quantum chaos.
  arXiv  Detail & Related papers  (2024-10-21T10:56:49Z)
• Sudden change in entanglement Hamiltonian: Phase diagram of an Ising entanglement Hamiltonian [10.721377880670696]
  We study the phase diagram of a 1D Ising entanglement Hamiltonian as an example to clarify the controversy of the general relation between the entanglement Hamiltonian and original Hamiltonian.
  arXiv  Detail & Related papers  (2024-10-14T02:13:34Z)
• The Aharonov-Bohm Hamiltonian: self-adjointness, spectral and scattering properties [0.0]
  This work provides an introduction and overview on some basic mathematical aspects of the single-flux Aharonov-Bohm Schr"odinger operator. The whole family of self-adjoint realizations is characterized by means of four different methods. Special attention is devoted to those self-adjoint realizations which preserve the same rotational symmetry and homogeneity under dilations of the basic differential operator.
  arXiv  Detail & Related papers  (2024-07-21T10:51:52Z)
• Quantum Chaos on Edge [36.136619420474766]
  We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension. While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
  arXiv  Detail & Related papers  (2024-03-20T11:31:51Z)
• Hearing the boundary conditions of the one-dimensional Dirac operator [0.0]
  We study the isospectrality problem for a relativistic free quantum particle, described by the Dirac Hamiltonian, confined in a one-dimensional ring with a junction.
  arXiv  Detail & Related papers  (2023-11-29T11:48:46Z)
• 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)
• Eigenstate thermalization hypothesis through the lens of autocorrelation functions [0.0]
  Matrix elements of observables in eigenstates of generic Hamiltonians are described by the Srednicki ansatz. We study a quantum chaotic spin-fermion model in a one-dimensional lattice.
  arXiv  Detail & Related papers  (2020-11-27T19:05:32Z)
• Extensions of Hardy-type true-implies-false gadgets to classically obtain indistinguishability [0.0]
  Hardy-type arguments can be uniformly presented and extended as collections of intertwined contexts and their observables. They serve as graph-theoretic "gadgets" that enforce correlations on the respective preselected and postselected observable terminal points.
  arXiv  Detail & Related papers  (2020-06-22T10:43:15Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)

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.