Thermodynamic Properties of the Dunkl-Pauli Oscillator in an Aharonov-Bohm Flux

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 Hilbert space is restructured rather than merely shifted in energy. Using the exact spectrum, we construct the partition function and derive the internal energy, entropy, and heat capacity. The thermodynamic quantities directly reflect this spectral constraint: the low-temperature behavior is governed by $\ell_0$, and the heat capacity exhibits a flux-controlled Schottky anomaly. At high temperatures, the classical oscillator limit is recovered. Our results show that the interplay between Dunkl symmetry and AB flux qualitatively modifies the set of admissible states, with observable thermodynamic signatures.