Time-Dependent Dunkl-Pauli Oscillator in the Presence of the Aharonov-Bohm Effect

• URL: http://arxiv.org/abs/2601.03365v2
• Date: Tue, 13 Jan 2026 10:43:10 GMT
• Title: Time-Dependent Dunkl-Pauli Oscillator in the Presence of the Aharonov-Bohm Effect
• Authors: Boubakeur Khantoul, Ahmed Tedjani,
• Abstract summary: We derive a deformed Pauli Hamiltonian that encodes reflection symmetries and topological gauge phases.<n>Our framework reveals novel spectral characteristics arising from the interplay between topology and Dunkl symmetry.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present an exact, time-dependent solution for a two-dimensional Pauli oscillator deformed by Dunkl operators in the presence of an Aharonov--Bohm (AB) flux. By replacing conventional momenta with Dunkl momenta and allowing arbitrary time dependence in both, mass and frequency, we derive a deformed Pauli Hamiltonian that encodes reflection symmetries and topological gauge phases. Employing the Lewis-Riesenfeld invariant method, we derive exact expressions for the eigenvalues and spinor eigenfunctions of the system. Crucially, the AB flux imposes symmetry constraints on the Dunkl parameters of the form $ν_1 = \mp ν_2 $, linking the reflection symmetry ($ε= \pm 1 $) to the quantization of angular momentum. These constraints modify the energy spectrum and wavefunctions of the angular operator and the invariant operator. Our framework reveals novel spectral characteristics arising from the interplay between topology and Dunkl symmetry, with potential implications for quantum simulation in engineered systems such as cold atoms and quantum dots.

Related papers

• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Constructive interference at the edge of quantum ergodic dynamics [116.94795372054381]
  We characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC$(2)$.<n>In contrast to dynamics without time reversal, OTOC$(2)$ are observed to remain sensitive to the underlying dynamics at long time scales.
  arXiv  Detail & Related papers  (2025-06-11T21:29:23Z)
• Quantum simulation of elastic wave equations via Schrödingerisation [26.502965344680117]
  We study quantum simulation algorithms on the elastic wave equations using the Schr"odingerisation method.<n>For the velocity-stress equation in isotropic media, we explore the symmetric matrix form under the external forcing via Schr"odingerisation combined with spectral method.<n>For the wave displacement equation, we transform it into a hyperbolic system and apply the Schr"odingerisation method, which is then discretized by the spectral method and central difference scheme.
  arXiv  Detail & Related papers  (2025-05-24T14:16:39Z)
• 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)
• Time-dependent Dunkl-Pauli Oscillator [0.0]
  We construct the Dunkl-Pauli Hamiltonian, which incorporates a time-varying magnetic field and a harmonic oscillator characterized by time-dependent mass and frequency. Our findings regarding the total quantum phase factor and wave functions reveal the significant impact of Dunkl operators on quantum systems.
  arXiv  Detail & Related papers  (2024-10-24T07:38:02Z)
• Generalized Duffin-Kemmer-Petiau oscillator under Aharonov-Bohm flux in topological defects backgrounds [8.685496600907996]
  We study the generalized Duffin-Kemmer-Petiau (DKP) oscillator under the influence of quantum flux field. It is shown that the energy eigenvalues are influenced by the topological defect of cosmic string and point-like global monopole.
  arXiv  Detail & Related papers  (2024-02-02T05:25:46Z)
• Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches [41.94295877935867]
  We study the melting of charge-density waves in a Holstein model after a sudden switch-on of the electronic hopping. A comparison with exact data obtained for a Holstein chain shows that a semiclassical treatment of both the electrons and phonons is required in order to correctly describe the phononic dynamics.
  arXiv  Detail & Related papers  (2023-12-19T16:14:01Z)
• Linear Response for pseudo-Hermitian Hamiltonian Systems: Application to PT-Symmetric Qubits [0.0]
  We develop the linear response theory formulation suitable for application to various pHH systems. We apply our results to two textitPT-symmetric non-Hermitian quantum systems.
  arXiv  Detail & Related papers  (2022-06-18T10:05:30Z)
• An introduction to PT-symmetric quantum mechanics -- time-dependent systems [0.0]
  I will provide a pedagogical introduction to non-Hermitian quantum systems that are PT-symmetric. I will explain how generalised versions of this antilinear symmetry can be utilised to explain that these type of systems possess real eigenvalue spectra in parts of their parameter spaces. I will explain how to extend this framework to explicitly time-dependent Hamiltonian systems.
  arXiv  Detail & Related papers  (2022-01-13T18:52:30Z)
• 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)
• Effects of quenching protocols based on parametric oscillators [2.363392878776903]
  We focus on the case where $omega(t)2$ behaves like a Morse potential, up to possible sign reversion and translations in the $(t,omega2)$ plane. We provide an insight on the way quantum states evolve by paying attention on the position-momentum Heisenberg uncertainty principle and the statistical aspects implied by second-order correlation functions over number-type states.
  arXiv  Detail & Related papers  (2020-07-04T17:37:36Z)
• Equivalence of approaches to relational quantum dynamics in relativistic settings [68.8204255655161]
  We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
  arXiv  Detail & Related papers  (2020-07-01T16:12:24Z)
• Driving Quantum Correlated Atom-Pairs from a Bose-Einstein Condensate [0.0]
  We investigate one such control protocol that demonstrates the resonant amplification of quasimomentum pairs from a Bose-Einstein condensate. A classical external field that excites pairs of particles with the same energy but opposite momenta is reminiscent of the coherently-driven nonlinearity in a parametric amplifier crystal.
  arXiv  Detail & Related papers  (2020-01-08T00:11:26Z)

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.