On Dunkl-Bose-Einstein Condensation in Harmonic Traps

Abstract

The use of the Dunkl derivative, which is defined by a combination of the difference-differential and reflection operator, 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 a similar 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 and finally 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. The Wigner parameter of the Dunkl formalism can be successfully used to obtain a better agreement between experimental and theoretical results.

arXiv comment11 pages, 5 figures

References in corpus (17)

• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• Exact operator solution of the Calogero-Sutherland model
• Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
• Bose-Einstein Condensation in a Harmonic Potential
• Bose-Einstein condensation of atomic gases in a harmonic oscillator confining potential trap
• Deformed Heisenberg algebra with reflection
• The Dunkl oscillator in the plane II : representations of the symmetry algebra
• Common Algebraic Structure for the Calogero-Sutherland Models
• Exact Solutions of the 2D Dunkl--Klein--Gordon Equation: The Coulomb Potential and the Klein--Gordon Oscillator
• Hidden nonlinear supersymmetries in pure parabosonic systems
• Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential
• Rigorous Hamiltonian and Lagrangian analysis of classical and quantum theories with minimal length
• Thermal Properties of Relativistic Dunkl Oscillators
• Dunkl-Graphene in constant magnetic field
• Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
• The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic
• Thermodynamics of bosons systems related to Dunkl differential-difference operators

Cited by in corpus (6)

• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• The Condensation of Ideal Dunkl-Bose Gas in Power-Law Traps
• One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
• Bounding the Wigner Deformation Parameter in Harmonically Trapped Bose Gases
• Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications