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arXiv:2603.09364

Dunkl--Pauli Oscillator in an Aharonov--Bohm Flux: Restriction of Admissible Angular Sectors and Thermodynamic Signatures

Ahmed Tedjani, Boubakeur Khantoul

quant-phSubmitted Mar 10, 2026• Announced Mar 11, 2026• 0 citations• Revised Aug 24, 2026 (v3)
v1 · Mar 10, 2026v2 · Apr 13, 2026v3 · Aug 24, 2026
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Abstract

We study a two-dimensional Dunkl--Pauli oscillator in the presence of an Aharonov--Bohm (AB) flux. The combination of reflection symmetry (via Dunkl operators) and a topological gauge field imposes a nontrivial constraint on the admissible quantum states: the regularity condition on radial wave functions, together with the matching conditions at the flux tube, leads to a compatibility relation $ν_1+\varepsilonν_2=0$ and forces the emergence of a lowest angular quantum number~$\ell_0$. As a result, the admissible angular sectors are restricted rather than the spectrum being merely shifted in energy. Using the exact spectrum, we construct the canonical partition function and derive closed-form expressions for the internal energy, entropy, and heat capacity. The thermodynamic quantities directly reflect this spectral constraint: the low-temperature behaviour is governed by~$\ell_0$, and the heat capacity exhibits a flux-controlled Schottky-like peak. The Dunkl parameter~$ν$ plays a dual role: within a fixed sector it shifts the energy scale, while globally it controls the flux threshold that determines which sectors are admissible. At high temperatures the classical two-dimensional oscillator limit is recovered. Our results demonstrate that the interplay between Dunkl symmetry and AB flux qualitatively modifies the set of admissible states, with observable thermodynamic signatures.

Comments
17 pages , 6 figures

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We study a two-dimensional Dunkl--Pauli oscillator in the presence of an Aharonov--Bohm (AB) flux. The combination of reflection symmetry (via Dunkl operators) and a topological gauge field imposes a nontrivial constraint on the admissible quantum states: the regularity condition on radial wave functions, together with the matching conditions at the flux tube, leads to a compatibility relation ν1+εν2=0ν_1+\varepsilonν_2=0ν1​+εν2​=0 and forces the emergence of a lowest angular quantum number~ℓ0\ell_0ℓ0​. As a result, the admissible angular sectors are restricted rather than the spectrum being merely shifted in energy.
Using the exact spectrum, we construct the canonical partition function and derive closed-form expressions for the internal energy, entropy, and heat capacity. The thermodynamic quantities directly reflect this spectral constraint: the low-temperature behaviour is governed by~ℓ0\ell_0ℓ0​, and the heat capacity exhibits a flux-controlled Schottky-like peak. The Dunkl parameter~ννν plays a dual role: within a fixed sector it shifts the energy scale, while globally it controls the flux threshold that determines which sectors are admissible. At high temperatures the classical two-dimensional oscillator limit is recovered.
Our results demonstrate that the interplay between Dunkl symmetry and AB flux qualitatively modifies the set of admissible states, with observable thermodynamic signatures.
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 = ∓ ν 2 , linking the reflection symmetry ( ϵ = ± 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.
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 ,linkingthereflectionsymmetry(, linking the reflection symmetry (,linkingthereflectionsymmetry(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.
This work investigates a class of exactly solvable quantum systems described by a generalized Dunkl--Schrödinger equation with energy-dependent interactions. A two-parameter extension of the Dunkl differential operator is introduced, incorporating both the conventional reflection contribution and an additional derivative-reflection coupling. The resulting formalism leads to a modified Heisenberg algebra, from which the continuity equation, conserved probability current, and generalized normalization condition are derived for energy-dependent potentials. As an application, an energy-dependent harmonic oscillator is studied in detail. Exact analytical expressions for the eigenfunctions and energy spectrum are obtained in terms of associated Laguerre polynomials. The combined effects of the Wigner parameter, the deformation parameter, and the energy-dependence parameter are shown to produce parity splitting, nonlinear energy spectra, and nonuniform level spacing while preserving exact solvability. The thermodynamic properties of the model are then examined through the canonical partition function using the Euler--Maclaurin summation formula. Analytical expressions for the partition function, internal energy, entropy, and specific heat are derived and analyzed numerically. The results demonstrate that the generalized Dunkl deformation and energy-dependent interaction provide effective control over both the spectral and thermal characteristics of the system, extending the class of exactly solvable quantum models with reflection symmetry.
We investigate the thermo-magnetic properties of the Attractive Radial Potential (ARP) for a particle moving in two-dimensional non-relativistic Schrödinger equation subjected to an external magnetic field and Aharonov-Bohm (AB) flux. Analytical solution for the energy eigenvalues and wavefunctions were obtained in a closed form via the Nikiforov-Uvarov Functional Analysis (NUFA) method. We derived the partition function by analyzing the system as a canonical ensemble to obtain the expressions for the thermodynamic quantities which include the free energy, entropy, specific heat capacity and internal energy. Our results show a decrease in the energy spectrum when the AB flux and magnetic fields are increased. At low temperatures, specific heat capacity shows a peak anomaly, while Helmholtz free energy and entropy exhibit temperature dependence. We also observed that AB flux and magnetic field influence both magnetization and magnetic susceptibility and exhibit both paramagnetic and diamagnetic behavior. The findings provide valuable insights into in molecular physics applications.
We study a finite-width two-dimensional quantum ring with a quadratic ddd-wave altermagnetic term, Tan--Inkson confinement, a perpendicular magnetic field, and independently tunable Aharonov--Bohm (AB) flux. The altermagnetic interaction mixes mmm and m±2m\pm2m±2 angular channels while preserving their parity. Circular symmetry renders the crystal orientation spectrally irrelevant and makes the two spin blocks exactly isospectral. The resulting same-parity anticrossings are resolved at low filling, and multichannel mixing is found near the Fermi level of highly occupied rings. Independent converged calculations for Ne=1400N_e=1400Ne​=1400 and 180018001800 establish the reconstructed Fermi edge and magnetic response in a finite field window and the persistent current over a full AB flux period. The analytic conventional reference separates radial-subband depopulation (dHvA-type cycles) from finer finite-ring shell oscillations; we do not assign a global Fourier spectrum to unverified altermagnetic field scans. The few-electron thermal response is obtained from an exact fixed-particle-number canonical partition function, avoiding finite-system errors of a fixed-mean-number approximation. The circular model supports an equilibrium charge current but no persistent spin current.
The use of the Dunkl derivative, defined by a combination of the difference-differential and reflection operators, allows the classification of the solutions according to even and odd solutions. Recently, we considered the Dunkl formalism to investigate the Bose-Einstein condensation of an ideal Bose gas confined in a gravitational field. In this work, we address another essential problem and examine an ideal Bose gas trapped by a three-dimensional harmonic oscillator within the Dunkl formalism. To this end, we derive an analytic expression for the critical temperature of the N particle system, discuss its value at large-N limit andfinally derive and compare the ground state population with the usual case result. In addition, we explore two thermal quantities, namely the Dunkl-internal energy and the Dunkl-heat capacity functions.