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

TL;DR

This paper provides an exact solution for a time-dependent Dunkl-Pauli oscillator influenced by the Aharonov-Bohm effect, revealing how topology and reflection symmetries alter its spectral properties.

Contribution

It introduces a novel time-dependent Dunkl-Pauli oscillator model with exact solutions, incorporating topological and reflection symmetries through the Aharonov-Bohm flux.

Findings

Modified energy spectrum due to AB flux constraints

Exact eigenvalues and eigenfunctions derived

Spectral features influenced by Dunkl symmetry and topology

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 $\nu_1 = \mp \nu_2 $, linking the reflection symmetry ($\epsilon = \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.