Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2410.09646 · Journal of Statistical Mechanics Theory and Experiment

Bounding the Wigner deformation parameter in harmonically trapped Bose gases

Mohamed Benarous, A. Hocine, B. C. Lütfüoğlu, B. Hamil

Published May 1, 2025• 5 citations
arXivHTMLPDF

Abstract

Abstract By examining the internal energy and the heat capacity of a harmonically trapped ideal Bose gas within the Dunkl formalism, we show that the Wigner parameter influences the slopes of these thermodynamic functions in the critical region, reflecting its role in modifying the statistical properties of the system. However, despite these modifications, the phase transition itself retains the same order and critical exponents as in the standard case, in accordance with symmetry arguments. Furthermore, upon analyzing the classical behavior, we establish both upper and lower bounds for the Wigner parameter by ensuring thermodynamic consistency in different temperature regimes.

DOI
10.1088/1742-5468/add511

Related papers

Critical properties of weakly interacting Bose gases as modified by a harmonic confinement

I. Reyes-Ayala, Freddy Jackson Poveda-Cuevas, Jorge Amin Seman +1 more

Abstract The critical properties of the phase transition from a normal gas to a Bose–Einstein condensate (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas–Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the global thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.

arXiv:1607.02389•Journal of Statistical Mechanics Theory and Experiment•Jul 1, 2017•5 citations

Systematic semiclassical expansion for harmonically trapped ideal Bose gases

Axel Pelster, Physical Journal B, Axel Pelster

Abstract. Using a field-theoretic approach, we systematically generalize the usual semiclassical approximation for a harmonically trapped ideal Bose gas in such a way that its range of applicability is essentially extended. With this we can analytically calculate thermodynamic properties even for small particle numbers. In particular, it now becomes possible to determine the critical temperature as well as the temperature dependence of both heat capacity and condensate fraction in low-dimensional traps, where the standard semiclassical approximation is not even applicable. PACS. 03.65.Sq Semiclassical theories and applications – 03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties – 05.70.Ce Thermodynamic functions and equations of state 1

•Jan 1, 2009•18 citations

On Dunkl-Bose-Einstein Condensation in Harmonic Traps

A. Hocine, B. Hamil, F. Merabtine +2 more

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.

arXiv:2308.10891•Revista Mexicana de Física•Sep 1, 2024•12 citations

Universal Thermodynamics of Dunkl-Deformed Bose Gases: From Power-Law Traps to Physical Bounds

Medani, M., Mohamed Benarous, A. Hocine +1 more

We study an ideal Bose gas confined by a $D$-dimensional power-law potential within the framework of the Dunkl formalism. By analyzing the combined effects of spatial dimensionality and trap geometry, we derive universal expressions for the thermodynamic quantities, which depend solely on a single parameter. This reduction reveals the existence of universality classes that apply to any power-law potential, regardless of its specific form.

arXiv:2508.12124•Aug 16, 2025•0 citations

Phase transition of a Bose gas in a harmonic potential

K Damle, T. Senthil, Satya N. Majumdar +1 more

We consider a Bose gas confined by a harmonic potential. We define an appropriate thermodynamic limit and analyze the properties of the phases and phase transition in this limit. Critical properties in the presence of the potential are found to be different from, though simply related to, those in the usual translationally invariant case. We argue that the properties of magnetically trapped rubidium and sodium gases (in which Bose-Einstein condensation has recently been observed) are well approximated by our thermodynamic limit except in a narrow window of temperature around the critical temperature. We also consider the effect of the confining potential on the non-equilibrium dynamics following a rapid quench to the ordered side and give a scaling description of the late-time universal dynamics.

arXiv:cond-mat/9604037•Europhysics Letters (EPL)•Oct 1, 1996•47 citations

Critical exponents and fluctuations at BEC in a 2D harmonically trapped ideal gas

M. I. Morales-Amador, Vı́ctor Romero-Rochı́n, R. Paredes

Abstract The critical properties displayed by an ideal 2D Bose gas trapped in a harmonic potential are determined and characterized in an exact numerical fashion. Beyond thermodynamics, addressed in terms of the global pressure and volume which are the appropriate variables of a fluid confined in a non-uniform harmonic potential, the density-density correlation function is also calculated and the corresponding correlation length is found. Evaluation of all these quantities as Bose–Einstein condensation (BEC) is approached manifest its critical continuous phase transition character. The divergence of the correlation length as the critical temperature is reached, unveils the expected spatial scale invariance proper of a critical transition. The logarithmic singularities of this transition are traced back to the non-analytic behavior of the thermodynamic variables at vanishing chemical potential, which is the onset of BEC. The critical exponents associated with the ideal BEC transition in the 2D inhomogeneous fluid reveals its own universality class.

arXiv:2308.02744•Journal of Physics B Atomic Molecular and Optical Physics•Feb 12, 2024•2 citations
Abstract By examining the internal energy and the heat capacity of a harmonically trapped ideal Bose gas within the Dunkl formalism, we show that the Wigner parameter influences the slopes of these thermodynamic functions in the critical region, reflecting its role in modifying the statistical properties of the system. However, despite these modifications, the phase transition itself retains the same order and critical exponents as in the standard case, in accordance with symmetry arguments. Furthermore, upon analyzing the classical behavior, we establish both upper and lower bounds for the Wigner parameter by ensuring thermodynamic consistency in different temperature regimes.
Abstract The critical properties of the phase transition from a normal gas to a Bose–Einstein condensate (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas–Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the global thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.
Abstract. Using a field-theoretic approach, we systematically generalize the usual semiclassical approximation for a harmonically trapped ideal Bose gas in such a way that its range of applicability is essentially extended. With this we can analytically calculate thermodynamic properties even for small particle numbers. In particular, it now becomes possible to determine the critical temperature as well as the temperature dependence of both heat capacity and condensate fraction in low-dimensional traps, where the standard semiclassical approximation is not even applicable. PACS. 03.65.Sq Semiclassical theories and applications – 03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties – 05.70.Ce Thermodynamic functions and equations of state 1
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.
We study an ideal Bose gas confined by a DDD-dimensional power-law potential within the framework of the Dunkl formalism. By analyzing the combined effects of spatial dimensionality and trap geometry, we derive universal expressions for the thermodynamic quantities, which depend solely on a single parameter. This reduction reveals the existence of universality classes that apply to any power-law potential, regardless of its specific form.
We consider a Bose gas confined by a harmonic potential. We define an appropriate thermodynamic limit and analyze the properties of the phases and phase transition in this limit. Critical properties in the presence of the potential are found to be different from, though simply related to, those in the usual translationally invariant case. We argue that the properties of magnetically trapped rubidium and sodium gases (in which Bose-Einstein condensation has recently been observed) are well approximated by our thermodynamic limit except in a narrow window of temperature around the critical temperature. We also consider the effect of the confining potential on the non-equilibrium dynamics following a rapid quench to the ordered side and give a scaling description of the late-time universal dynamics.
Abstract The critical properties displayed by an ideal 2D Bose gas trapped in a harmonic potential are determined and characterized in an exact numerical fashion. Beyond thermodynamics, addressed in terms of the global pressure and volume which are the appropriate variables of a fluid confined in a non-uniform harmonic potential, the density-density correlation function is also calculated and the corresponding correlation length is found. Evaluation of all these quantities as Bose–Einstein condensation (BEC) is approached manifest its critical continuous phase transition character. The divergence of the correlation length as the critical temperature is reached, unveils the expected spatial scale invariance proper of a critical transition. The logarithmic singularities of this transition are traced back to the non-analytic behavior of the thermodynamic variables at vanishing chemical potential, which is the onset of BEC. The critical exponents associated with the ideal BEC transition in the 2D inhomogeneous fluid reveals its own universality class.