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

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 $\nu_1+\varepsilon\nu_2=0$ 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~$\nu$ 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.