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

Condensation in some perturbed meanfield models of a Bose gas

T. C. Dorlas, Thomas Lewis, Pulé, J.V.

Published Dec 2, 1991• 3 citations
Publisher

Abstract

We examine the existence of Bose-Einstein condensation in a perturbed meanfield model of a Bose gas in which the interaction is given by a Gaussian kernel. We find that : for negative values of the chemical potential μ there is never condensation ; there is a μ 0 >0 such that for μ∈(0,μi0) there is condensation for all temperatures below a critical temperature T C (μ) ; there is a μ 0 >2μ 0 such that for μ∈(μ 0 ,μ 0 ) at sufficiently low temperatures, there is no condensation

DOI
10.5169/seals-116337

Related papers

Proof of Bose condensation for weakly interacting lattice bosons

Дмитрий Петрович Санкович

A weakly interacting Bose gas on a simple cubic lattice is considered. We prove the existence of the standard or zero-mode Bose condensation at sufficiently low temperature. This result is valid for sufficiently small interaction potential and small values of chemical potential. Our method exploits infrared bound for the suitable two-point Bogolyubov's inner product. We do not use the reflection positivity or some expansion methods.

arXiv:1806.01241•Journal of Physics Communications•Oct 1, 2018•1 citation

Bose-Einstein Condensation in Finite System

Zheng Yong

Based on grand canonical assembles statistics,the Bose Einstein Condensation (BEC) in non interacting bound atomic system is studied.Some basic concepts of BEC in conventional infinite Bose system are extended.The condition of chemical potential μ ≤0 will not be guarantted for the present finite bound system,and the vapour with μ 0,the state without condensation at any eigenstate,might be possible in principle even below a critical temperature T C .Gibbs functions for both the gas and the BEC state at temperature TT C have been calculated.The condition for BEC to appear is presented.The relation of BEC temperature T C with the density of particles is estimated and the result is qualitatively in good agreement with the experimental results.

Fudan xuebao. Ziran Kexue ban•Jan 1, 2002•0 citations

GAUSSIAN DOMINATION AND BOSE–EINSTEIN CONDENSATION IN THE INTERACTING BOSON GAS

M. Corgini, Дмитрий Петрович Санкович

A Davies model of an imperfect boson gas is considered. The model includes not only a convex, but also a concave type of an interaction function which depends on a dencity operator. A sufficient condition of the Bose–Einstein condensation is proved. An exact value of the critical temperature is obtained.

International Journal of Modern Physics B•Oct 30, 1999•1 citation

Bose-Einstein condensation in a one-dimensional interacting system due to power-law trapping potentials

Mehmet Bayındır, B. Tanatar, Z. Gedik

We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form ${V}_{\mathrm{ext}}{(x)=V}_{0}(|x|{/a)}^{\ensuremath{\gamma}},$ in which $\ensuremath{\gamma}<2,$ by solving the Gross-Pitaevskii equation within the semiclassical two-fluid model. The condensate fraction, chemical potential, ground state energy, and specific heat of the system are calculated for various values of interaction strengths. Our results show that a significant fraction of the particles is in the lowest energy state for a finite number of particles at low temperature, indicating a phase transition for weakly interacting systems.

arXiv:cond-mat/9810197•Physical Review A•Feb 1, 1999•17 citations

Approaching Bose–Einstein condensation

L. Ferrari

Bose–Einstein condensation (BEC) is discussed at the level of an advanced course of statistical thermodynamics, clarifying some formal and physical aspects that are usually not covered by the standard pedagogical literature. The non-conventional approach adopted starts by showing that the continuum limit, in certain cases, cancels out the crucial role of the bosonic ground level. If so, a correct treatment of the problem, including the ground level population N 0 by construction, leads to BEC in a straightforward way. For a density of states of the form G ( )∝ γ , the chemical potential µ is explicitly calculated as a function of the temperature T and of the number N of bosons, for various significant values of the positive exponent γ. In the thermodynamic limit, in which the boson number N diverges and BEC is a sharp process, the chemical potential µ is a singular function of T at the critical temperature T B , determined by an appropriate critical exponent. The condensate population N 0 is studied analytically and numerically as a function of the temperature, for various values of N and for different γ. This provides an accurate description of the way BEC approaches the character of a sharp phase transition. Some aspects of the real experiments on BEC, involving a finite number of bosons, are also illustrated.

European Journal of Physics•Oct 4, 2011•5 citations

Finite-Temperature Bose-Einstein Condensation in Interacting Boson System

D. Anchishkin, Igor N Mishustin, Oleksandr S. Stashko +2 more

Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. It is shown that, for sufficiently strong attractive interactions, this system develops a first-order phase transition via the formation of a Bose condensate. An interesting prediction of the model is that the condensed phase is characterized by a constant total density of particles. It is shown that the energy density exhibits a jump at the critical temperature.

Ukrainian Journal of Physics•Dec 9, 2019•5 citations
We examine the existence of Bose-Einstein condensation in a perturbed meanfield model of a Bose gas in which the interaction is given by a Gaussian kernel. We find that : for negative values of the chemical potential μ there is never condensation ; there is a μ 0 >0 such that for μ∈(0,μi0) there is condensation for all temperatures below a critical temperature T C (μ) ; there is a μ 0 >2μ 0 such that for μ∈(μ 0 ,μ 0 ) at sufficiently low temperatures, there is no condensation
Based on grand canonical assembles statistics,the Bose Einstein Condensation (BEC) in non interacting bound atomic system is studied.Some basic concepts of BEC in conventional infinite Bose system are extended.The condition of chemical potential μ ≤0 will not be guarantted for the present finite bound system,and the vapour with μ 0,the state without condensation at any eigenstate,might be possible in principle even below a critical temperature T C .Gibbs functions for both the gas and the BEC state at temperature TT C have been calculated.The condition for BEC to appear is presented.The relation of BEC temperature T C with the density of particles is estimated and the result is qualitatively in good agreement with the experimental results.
We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form ${V}_{\mathrm{ext}}{(x)=V}_{0}(|x|{/a)}^{\ensuremath{\gamma}},$ in which $\ensuremath{\gamma}<2,$ by solving the Gross-Pitaevskii equation within the semiclassical two-fluid model. The condensate fraction, chemical potential, ground state energy, and specific heat of the system are calculated for various values of interaction strengths. Our results show that a significant fraction of the particles is in the lowest energy state for a finite number of particles at low temperature, indicating a phase transition for weakly interacting systems.
Bose–Einstein condensation (BEC) is discussed at the level of an advanced course of statistical thermodynamics, clarifying some formal and physical aspects that are usually not covered by the standard pedagogical literature. The non-conventional approach adopted starts by showing that the continuum limit, in certain cases, cancels out the crucial role of the bosonic ground level. If so, a correct treatment of the problem, including the ground level population N 0 by construction, leads to BEC in a straightforward way. For a density of states of the form G ( )∝ γ , the chemical potential µ is explicitly calculated as a function of the temperature T and of the number N of bosons, for various significant values of the positive exponent γ. In the thermodynamic limit, in which the boson number N diverges and BEC is a sharp process, the chemical potential µ is a singular function of T at the critical temperature T B , determined by an appropriate critical exponent. The condensate population N 0 is studied analytically and numerically as a function of the temperature, for various values of N and for different γ. This provides an accurate description of the way BEC approaches the character of a sharp phase transition. Some aspects of the real experiments on BEC, involving a finite number of bosons, are also illustrated.
Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. It is shown that, for sufficiently strong attractive interactions, this system develops a first-order phase transition via the formation of a Bose condensate. An interesting prediction of the model is that the condensed phase is characterized by a constant total density of particles. It is shown that the energy density exhibits a jump at the critical temperature.