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Journal of Baoji University of Arts and Sciences

The thermodynamic properties of two-dimensional Bose gas in the q distribution

Weiyan Li

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Aim Based on the generalized Bose-Einstein distribution function in nonextensive statistical mechanics,thermodynamical quantities of the two-dimensional Bose gas such as internal energy,entropy,free energy,heat capacity,etc.,are calculated. Methods The factorization approach is incorporated,and the ensuing statistics is derived. Results/Conclusion Comparing these results with those of the conventional Bose statistics,it is found that the thermodynamical quantities are of similar forms.In the limit q→1,the thermodynamical quantities of the generalized two-dimensional Bose gas will return to the results of the Bose statistics.

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The thermodynamic properties of an ideal q-boson gas trapped in an n-dimensional harmonic potential are studied, based on the distribution function of q-bosons. The critical temperature Tc,q of Bose-Einstein condensation (BEC) and the heat capacity C of the system are derived analytically. It is shown that for the q-boson gas trapped in a harmonic potential, BEC may occur in any dimension when q ≠ 1, the critical temperature is always higher than that of an ordinary Bose gas (q = 1), and the heat capacity is continuous at Tc,q for a one-dimensional system but discontinuous at Tc,q for a two- or multi-dimensional system.
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This study aims to determine the thermodynamic properties of a paraboson system of order two. The thermodynamic properties to be searched include the grand canonical partition function (GCPF), Z , and the average number of particles, N . These parastatistics systems is a more general form compared to a quantum statistical distribution that has been known previously, i.e. Bose-Einstein statistics (BE). Starting from the recursion relation of the GCPF for paraboson system of order two, recursion linkages for some simple thermodynamic functions for paraboson system of order two may be derived. The recursion linkages are then used to calculate the thermodynamic function of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. The results from Z show that the thermodynamics properties of the paraboson system of order two can be derived and have a similar shape with paraboson system of order one (boson). The similarity of the graph shows similar thermodynamic properties.