Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Ahmed Tedjani, Boubakeur Khantoul

Abstract

We investigate the thermodynamic properties of a spin-$\frac{1}{2}$ particle described by the Dunkl-deformed Pauli equation in two dimensions in the presence of an Aharonov--Bohm (AB) flux. By replacing the standard momentum operators with Dunkl operators, the Hamiltonian incorporates reflection symmetry together with topological gauge effects. The magnetic flux imposes symmetry constraints on the Dunkl parameters, $ν_1 + \varepsilon ν_2 = 0$, linking the reflection sectors ($\varepsilon = \pm 1$) to the structure of the energy spectrum. Using the exact spectrum, we construct the canonical partition function and derive the thermodynamic quantities including the internal energy, entropy, and heat capacity. The results show that the interplay between Dunkl reflection symmetry and the AB phase leads to distinctive thermal behavior. In particular, the heat capacity exhibits a Schottky-type anomaly controlled by the magnetic flux, while at high temperatures the system approaches the classical oscillator limit.

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

Abstract

We investigate the thermodynamic properties of a spin- particle described by the Dunkl-deformed Pauli equation in two dimensions in the presence of an Aharonov--Bohm (AB) flux. By replacing the standard momentum operators with Dunkl operators, the Hamiltonian incorporates reflection symmetry together with topological gauge effects. The magnetic flux imposes symmetry constraints on the Dunkl parameters, , linking the reflection sectors () to the structure of the energy spectrum. Using the exact spectrum, we construct the canonical partition function and derive the thermodynamic quantities including the internal energy, entropy, and heat capacity. The results show that the interplay between Dunkl reflection symmetry and the AB phase leads to distinctive thermal behavior. In particular, the heat capacity exhibits a Schottky-type anomaly controlled by the magnetic flux, while at high temperatures the system approaches the classical oscillator limit.
Paper Structure (19 sections, 46 equations, 5 figures)

This paper contains 19 sections, 46 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Dunkl–Pauli Hamiltonian with Aharonov–Bohm Flux
  3. Aharonov–Bohm Configuration
  4. Dunkl Deformation of the Momentum Operator
  5. Explicit Form of the Dunkl–Pauli Hamiltonian
  6. Separation in Polar Coordinates
  7. Angular Eigenvalue Problem
  8. Even sector $\epsilon = +1$ ($\epsilon_1 = \epsilon_2 = \pm 1$):
  9. Odd sector $\epsilon = -1$ ($\epsilon_1 = -\epsilon_2$):
  10. Radial Equation and Regularization
  11. Radial Solutions and Matching Conditions
  12. Final Spectrum and Wave Functions
  13. Thermodynamic Properties
  14. Partition Function
  15. Internal Energy.
  16. ...and 4 more sections

Figures (5)

  • Figure 2: Temperature dependence of $Z(T)$ for $\varepsilon=-1$ and several values of the Dunkl parameter $\nu$ and the AB flux $\vartheta$.
  • Figure 3: Temperature dependence of internal energy $U(T)$ for $\varepsilon=+1$ and several values of the AB flux $\vartheta$.
  • Figure 4: Temperature dependence of internal energy $U(T)$ for $\varepsilon=-1$ and several values of the Dunkl parameter $\nu$ and the AB flux $\vartheta$.
  • Figure 5: Temperature dependence of $S(T)$ for several values of the AB flux $\vartheta$.
  • Figure 6: Heat Capacity $C_V(T)$ for several values of the AB flux $\vartheta$.