Quantum Systems with jump-discontinuous mass. I

• URL: http://arxiv.org/abs/2505.16913v2
• Date: Tue, 03 Jun 2025 09:57:23 GMT
• Title: Quantum Systems with jump-discontinuous mass. I
• Authors: Fabio Deelan Cunden, Giovanni Gramegna, Marilena Ligabò,
• Abstract summary: We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities.<n>For a family of scale-free boundary conditions, we analyse the associated spectral problem.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is realised as a self-adjoint extension of the kinetic energy operator formulated in divergence form, with the extension encoded in the boundary conditions at the mass discontinuity points. For a family of scale-free boundary conditions, we analyse the associated spectral problem. We find that the eigenfunctions exhibit a highly sensitive and erratic dependence on the energy, leading to irregular spectral behaviour. Notably, the system supports infinitely many distinct semiclassical limits, each labeled by a point on a spectral curve embedded in the two-torus. These results demonstrate a rich interplay between discontinuous coefficients, boundary data, and spectral asymptotics.

Related papers

• Robust quantification of spectral transitions in perturbed quantum systems [0.0]
  A quantum system can experience leakage between uncoupled regions of its energy spectrum separated by a gap.<n>We establish time-independent bounds on the distances between the true dynamics and the dynamics generated by block-diagonal effective evolutions.<n>We prove that, under the right conditions, this leakage remains small eternally.
  arXiv  Detail & Related papers  (2025-05-26T12:33:07Z)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Spread and Spectral Complexity in Quantum Spin Chains: from Integrability to Chaos [0.0]
  We explore spread and spectral complexity in quantum systems that exhibit a transition from integrability to chaos. We find that the saturation value of spread complexity post-peak depends not only on the spectral statistics of the Hamiltonian, but also on the specific state. We conjecture that the thermofield double state (TFD) is suitable for probing signatures of chaos in quantum many-body systems.
  arXiv  Detail & Related papers  (2024-05-18T10:54:50Z)
• 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)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Observation of partial and infinite-temperature thermalization induced by repeated measurements on a quantum hardware [62.997667081978825]
  We observe partial and infinite-temperature thermalization on a quantum superconducting processor. We show that the convergence does not tend to a completely mixed (infinite-temperature) state, but to a block-diagonal state in the observable basis.
  arXiv  Detail & Related papers  (2022-11-14T15:18:11Z)
• In-Gap Band Formation in a Periodically Driven Charge Density Wave Insulator [68.8204255655161]
  Periodically driven quantum many-body systems host unconventional behavior not realized at equilibrium. We investigate such a setup for strongly interacting spinless fermions on a chain, which at zero temperature and strong interactions form a charge density wave insulator.
  arXiv  Detail & Related papers  (2022-05-19T13:28:47Z)
• Spectral form factor in a minimal bosonic model of many-body quantum chaos [1.3793594968500609]
  We study spectral form factor in periodically-kicked bosonic chains. We numerically find a nontrivial systematic system-size dependence of the Thouless time.
  arXiv  Detail & Related papers  (2022-03-10T15:56:24Z)
• On the exactly-solvable semi-infinite quantum well of the non-rectangular step-harmonic profile [0.0]
  The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. We show that wavefunctions of the discrete spectrum recover wavefunctions in terms of the Hermites. We also present a new limit relation that reduces Bessels directly to Hermites.
  arXiv  Detail & Related papers  (2021-11-07T12:23:17Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.