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

Journal of Xiamen University

Critical Temperature and Ground State Fraction of a Weakly Interacting Bose Gas Trapped in a Harmonic Potential

Lixuan Chen

Published Jan 1, 2002• 1 citation
OpenAlex

Abstract

The critical temperature for the Bose-Einstein Condensation of an imperfect Bose gas trapped in a harmonic potential is calculated by using the local density approximation (LDA). The effects of weak interaction on the critical temperature and ground-state fraction of particles are discussed. The investigation will be helpful for the further understanding of the properties of BEC, which is called as a new kind of state of matter.

Related papers

Thermodynamic Properties of a Weakly Interacting Bose Gas Trapped in a Harmonic Potential

Lixuan Chen

The thermodynamic properties of a weakly interacting Bose gas trapped in a harmonic potential are studied based on the local-density approximation (LDA). The spatial distributions of particle number and energy and the expressions of some important thermodynamic quantities are derived analytically. The effects of the interatomic interaction on the thermodynamic properties of the system are discussed.

Journal of Xiamen University•Jan 1, 2003•1 citation

Bose Einstein condensation of gases in a harmonic potential trap

M. E. Zomorrodian, رمضانعلی سبیلی

One of the most interesting properties of boson gases is that under special conditions, there is a possibility of a phase transition, in a critical temperature below which all bosons condensate into the ground state. This phenomenon is called Bose – Einstein Condensation (BEC). In this paper, we investigate BEC in a harmonic oscillator trap. We conclude that, in contrast to a free boson gas, there is no critical temperature for phase transition in a harmonic oscillator trap. However , by numerical and analytical calculation, it is possible to obtain a temperature at which the heat capacity is maximum. We call this the critical temperature . Possible explanation for all these features will be explained in this paper.

•Mar 1, 2005•0 citations

Critical temperature and condensate fraction of a bose – einstein condensate trapped in a finite volume

AK Mukoya, T. W. Sakwa, K. M. Khanna +4 more

Bose - Einstein Condensation, BEC, of an ideal gas is investigated for a finite number of particles trapped in a harmonic potential. The values of the critical temperature for Rb-87, its condensate fraction and the energy per particle are determined. The maxima appear to increase with the number of particles due to the fact that a smaller system has a larger available effective volume which concurs with the behavior of the critical temperatures.

•Jan 1, 2014•0 citations

Bose-Einstein Condensation of an Ideal Bose Gas Trapped in the Low Dimensional Space

Liu Jing-yi

By using the local density approximation, Bose-Einstein condensation of Bose gas in the low dimensional space is investigated. The results show that when a proper external potential is taken, BEC may occur in the low dimensional space. The critical temperature Tc, the ground state fraction N0/N and the behaviour (jump or not) of the heat capacity C depend on the shape of the potential.

Journal of Zhangzhou Normal University•Jan 1, 2001•0 citations

Thermodynamics of rotating weakly interacting Bose gases in a harmonic trap

Yushan Li

The analytical expressions of particle number, critical temperature, condensate fraction, total energy, specific heat and spatial distribution of particle current for rotating weakly interacting Bose gases in a harmonic trap are derived by using the local density approximation (LDA). The effects of weakly repulsive interaction on the above thermodynamics are discussed by introducing a positive scattering length. Our results completely coincide with those for the case of rotating ideal Bose gases when the weak interaction disappears.

Modern Physics Letters B•Jun 21, 2019•1 citation

BOSE-EINSTEIN CONDENSATION IN TRAPS: A QUANTUM MONTE CARLO STUDY

Jonathan L. DuBois

We evaluate the zero temperature properties and Bose-Einstein condensation (BEC) of hard sphere bosons in a harmonic trap using Quantum Monte Carlo methods. The chief purpose of this work is to go beyond the dilute limit, to test the limits of the Gross-Pitaevskii equation and related mean field approximations and to explore the role of interactions in determining the zero temperature properties of the trapped Bose gas. The density is increased by adjusting both the number of trapped bosons, N , and the s-wave scattering length, a, to study systems from the highly dilute region corresponding to early experiments in trapped BEC [2, 3] up to liquid He densities and beyond. Rather than relying on the perturbative Bogoliubov approximation (which assumes a large condensate fraction) to describe the condensate, we use the one-body density matrix (OBDM) formulation of BEC so that the properties of the condensate for systems with arbitrarily large interactions may be studied. In this formulation of BEC, condensate properties are obtained by diagonalizing the OBDM and obtaining the corresponding single particle “natural orbitals” and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital(s) with macroscopic occupation (N0 >> 1). Within this framework, we calculate the effects of interactions and increased density on the ground state energy, the density profile, the momentum distribution, the condensate fraction and condensate “wave-function” and several other properties.

•Jan 1, 2002•1 citation
The critical temperature for the Bose-Einstein Condensation of an imperfect Bose gas trapped in a harmonic potential is calculated by using the local density approximation (LDA). The effects of weak interaction on the critical temperature and ground-state fraction of particles are discussed. The investigation will be helpful for the further understanding of the properties of BEC, which is called as a new kind of state of matter.
One of the most interesting properties of boson gases is that under special conditions, there is a possibility of a phase transition, in a critical temperature below which all bosons condensate into the ground state. This phenomenon is called Bose – Einstein Condensation (BEC). In this paper, we investigate BEC in a harmonic oscillator trap. We conclude that, in contrast to a free boson gas, there is no critical temperature for phase transition in a harmonic oscillator trap. However , by numerical and analytical calculation, it is possible to obtain a temperature at which the heat capacity is maximum. We call this the critical temperature . Possible explanation for all these features will be explained in this paper.
The analytical expressions of particle number, critical temperature, condensate fraction, total energy, specific heat and spatial distribution of particle current for rotating weakly interacting Bose gases in a harmonic trap are derived by using the local density approximation (LDA). The effects of weakly repulsive interaction on the above thermodynamics are discussed by introducing a positive scattering length. Our results completely coincide with those for the case of rotating ideal Bose gases when the weak interaction disappears.
We evaluate the zero temperature properties and Bose-Einstein condensation (BEC) of hard sphere bosons in a harmonic trap using Quantum Monte Carlo methods. The chief purpose of this work is to go beyond the dilute limit, to test the limits of the Gross-Pitaevskii equation and related mean field approximations and to explore the role of interactions in determining the zero temperature properties of the trapped Bose gas. The density is increased by adjusting both the number of trapped bosons, N , and the s-wave scattering length, a, to study systems from the highly dilute region corresponding to early experiments in trapped BEC [2, 3] up to liquid He densities and beyond. Rather than relying on the perturbative Bogoliubov approximation (which assumes a large condensate fraction) to describe the condensate, we use the one-body density matrix (OBDM) formulation of BEC so that the properties of the condensate for systems with arbitrarily large interactions may be studied. In this formulation of BEC, condensate properties are obtained by diagonalizing the OBDM and obtaining the corresponding single particle “natural orbitals” and their occupation numbers for the system. The condensate wave function and condensate fraction are then obtained from the single particle orbital(s) with macroscopic occupation (N0 >> 1). Within this framework, we calculate the effects of interactions and increased density on the ground state energy, the density profile, the momentum distribution, the condensate fraction and condensate “wave-function” and several other properties.