Physics – Condensed Matter – Quantum Gases
Scientific paper
2010-07-28
Physics
Condensed Matter
Quantum Gases
reference added in version 2
Scientific paper
We report calculation of critical exponents corresponding to three thermodynamic func- tions, viz. chemical potential, condensate fraction and specific heat of a non-interacting Bose gas confined in an isotropic harmonic oscillator trap in one-, two- and three- dimensions. Critical exponents are also calculated for bosons interacting through van der Waals potential and confined in a three-dimensional harmonic trap. These expo- nents are found to be independent of the size of the system and whether the bosons are interacting or not, demonstrating their universality property. We also find that a continuous phase transition occurs even in one-dimension, as shown by a rapid change of the thermodynamic functions at the critical point. This is in sharp contrast with the result found in the text book treatment of replacing the sum over occupations of discrete states by an integral. The two- and three-dimensional results agree with the well known results in the thermodynamic limit, i.e. when the number of bosons in the trap approaches infinity. In the same limit, the criticality disappears for the one-dimensional trap, which again agrees with the standard result.
Biswas Anindya
Das Tapan Kumar
Goswami Sanchari
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