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Journal of Physics Conference Series

Thermodynamic Functions of a Parabosonic System of Second Order

R Y A Sari, Wipsar Sunu Brams Dwandaru

Published Nov 1, 2017• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/909/1/012019

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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.
This study aims to determine the thermodynamic properties of the parastatistics 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 in a more general form compared to quantum statistical distribution that has been known previously, i.e.: the Fermi-Dirac (FD) and Bose-Einstein (BE). Starting from the recursion relation of grand canonical partition function for parastatistics system of order two that has been known, recuresion linkages for some simple thermodynamic functions for parastatistics system of order two are derived. The recursion linkages are then used to calculate the thermodynamic functions of the model system of identical particles with limited energy levels which is similar to the harmonic oscillator. From these results we concluded that from the Grand Canonical Partition Function (GCPF), Z, the thermodynamics properties of parastatistics system of order two (paraboson and parafermion) can be derived and have similar shape with parastatistics system of order one (Boson and Fermion). The similarity of the graph shows similar thermodynamic properties. Keywords: parastatistics, thermodynamic properties
For many-particle quantum systems, calculating thermodynamic quantities in the canonical ensemble is a very hard task, while this is tractable in the grand canonical ensemble.The second ensemble is then used.The results are supposed to be the same, at least in the thermodynamic limit.Is this actually the case?In this work, we consider a system of N noninteracting bosons distributed among few energy levels.We can calculate the canonical partition function in this case and deduce the canonical mean energy.We compare it to the mean energy deduced from the grand canonical ensemble for the same number of particles.We consider the case of a large number of particles.
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.
We derive an exact recursion formula for the calculation of thermodynamic functions of finite systems obeying Bose-Einstein statistics. The formula is applicable for canonical systems where the particles can be treated as noninteracting in some approximation, e.g., like Bose-Einstein condensates in magnetic traps. The numerical effort of our computation scheme grows only linearly with the number of particles. As an example, we calculate the relative ground-state fluctuations and specific heats for ideal Bose gases with a finite number of particles enclosed in containers of different shapes.
For ideal Bose atoms in an isotropic harmonic trap, we consider thermodynamic variables obtained from microcanonical, canonical, and grand canonical ensembles, each with certain variables specified and other variables fluctuating. For the first two of these ensembles, we derive recursion relations that link partition functions for different dimensions. We discuss fluctuations in general, and obtain expressions for variances of the atom number N, the chemical potential \ensuremath{\mu}, and the temperature T for small, Gaussian fluctuations in the grand canonical ensemble. Then from our recursion relations and others given elsewhere, we obtain probability distributions for N, for ground-state occupation number n0{n}_{0}n0​, for \ensuremath{\mu}, and for T. Below the critical temperature, the shape of the distributions for N, n0,{n}_{0},n0​, and \ensuremath{\mu} are definitely not Gaussian for the grand canonical ensemble. For given temperature and small N, we find that the chemical potential values pertaining to the three ensembles differ. We compare the specific-heat function CN(T){C}_{N}(T)CN​(T) for the three ensembles and propose to use the minimum of dCN/dT{\mathrm{dC}}_{N}/dTdCN​/dT to define the critical temperature to facilitate comparisons with similar configurations of interacting atoms.