The phase transition of the one-dimensional Bose gas, interacting weakly with a repulsive potential and trapped in an external parabolic potential, is studied in a mean field approximation. The Bose–Einstein condensed (BEC) state is identified by the non-vanishing thermal average of a bose field. Free energies between the BEC state and normal state are compared. A crossing of the free energies occurring at low temperature suggests the first order phase transition in an interacting one-dimensional bose system. From fitting of numerical results, the relation among the transition temperature T c , the total number of bosons N and the interaction V is also provided as a simple power law, T c ∝( N 2 V ) 2/3 .The phase transition of the one-dimensional Bose gas, interacting weakly with a repulsive potential and trapped in an external parabolic potential, is studied in a mean field approximation. The Bose–Einstein condensed (BEC) state is identified by the non-vanishing thermal average of a bose field. Free energies between the BEC state and normal state are compared. A crossing of the free energies occurring at low temperature suggests the first order phase transition in an interacting one-dimensional bose system. From fitting of numerical results, the relation among the transition temperature T c , the total number of bosons N and the interaction V is also provided as a simple power law, T c ∝( N 2 V ) 2/3 .

Journal of the Physical Society of JapanAug 1, 20021 citation

THEORETICAL ASPECTS OF BOSE–EINSTEIN CONDENSATION

Adelchi Fabrocini

Series on advances in quantum many-body theoryAug 1, 20020 citations

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.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, 20050 citations

Transition Temperatures of Bose–Einstein Condensation in Traps

Guangxi Hu, X.-X. Dai, J.-X. Dai +1 more

Journal of Low Temperature PhysicsOct 24, 20039 citations

FINITE-TEMPERATURE EFFECTS IN BOSE-EINSTEIN CONDENSATES

Keith R. Burnett

Dec 1, 20001 citation

Analysis of in situ images of Bose-Einstein condensates of lithium

C. C. Bradley, Charles A. Sackett, Randall G. Hulet

The initial evidence for Bose-Einstein condensation (BEC) of $^{7}\mathrm{Li}$ consisted of image distortions that suddenly appeared as the gas was evaporatively cooled to near the transition temperature. We present results of a model of the imaging system used to produce these images. The model confirms that the distortions are a sensitive indicator of BEC, but shows that they make quantitative analysis difficult. We find that the distortions resulted from light scattered by the condensate, in conjunction with aberrations in the imaging lens.The initial evidence for Bose-Einstein condensation (BEC) of $^{7}\mathrm{Li}$ consisted of image distortions that suddenly appeared as the gas was evaporatively cooled to near the transition temperature. We present results of a model of the imaging system used to produce these images. The model confirms that the distortions are a sensitive indicator of BEC, but shows that they make quantitative analysis difficult. We find that the distortions resulted from light scattered by the condensate, in conjunction with aberrations in the imaging lens.

Physical Review AMay 1, 199748 citations

The initial evidence for Bose-Einstein condensation (BEC) of

^{7}\mathrm{Li}

consisted of image distortions that suddenly appeared as the gas was evaporatively cooled to near the transition temperature. We present results of a model of the imaging system used to produce these images. The model confirms that the distortions are a sensitive indicator of BEC, but shows that they make quantitative analysis difficult. We find that the distortions resulted from light scattered by the condensate, in conjunction with aberrations in the imaging lens.