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 propertiesThis 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

Jurnal Sains DasarMay 20, 20160 citations

Canonical number projection in a simple nuclear model

DAVID M. VAN DER WALT, R. M. Quick

The heat capacity for a system of nucleons as a function of temperature is determined from the canonical partition function, which is projected from an approximation to the grand canonical partition function. This approximation is obtained from a functional integral representation of the partition function, including both thermodynamic fluctuations and first order quantum corrections. The number projection methods include a simple contour integration of ``Wick rotation'', and a Chebyschev polynomial expansion, both of which are formally exact. The above procedure is tested in a simple ${\mathit{i}}_{13/2}$ pairing model for which the exact canonical and grand canonical results can be obtained. It is found that both number projection methods fail to predict the position or the height of the peak in the heat capacity due to errors in the approximation to the grand partition function, even though the path integral approximation is very good.The heat capacity for a system of nucleons as a function of temperature is determined from the canonical partition function, which is projected from an approximation to the grand canonical partition function. This approximation is obtained from a functional integral representation of the partition function, including both thermodynamic fluctuations and first order quantum corrections. The number projection methods include a simple contour integration of ``Wick rotation'', and a Chebyschev polynomial expansion, both of which are formally exact. The above procedure is tested in a simple ${\mathit{i}}_{13/2}$ pairing model for which the exact canonical and grand canonical results can be obtained. It is found that both number projection methods fail to predict the position or the height of the peak in the heat capacity due to errors in the approximation to the grand partition function, even though the path integral approximation is very good.

Physical Review CApr 1, 19943 citations

Quantum corrections for general partition functions

L.R. Evangelista, Luís Carlos Malacarne, R.S. Mendes

arXiv:cond-mat/9804094Physica A Statistical Mechanics and its ApplicationsMay 1, 19988 citations

Grand Canonical Partition Function for Unidimensional Systems: Application to Hubbard Model up to Order beta^3

I. C. Charret, S. M. de Souza, M. T. Thomaz +1 more

We exploit the grassmannian nature of the variables involved in the path integral expression of the grand canonical partition function for self--interacting fermionic models to show, in one-space dimension, a general relation among the terms of it expansion in the high temperature limit and a combination of co-factors of a suitable matrix with commuting entries. As an application, we apply this framework to calculate the exact coefficients, up to order β^3, of the expansion of the grand canonical partition function for the Hubbard model in d=(1+1) in the high temperature limit. The results are valid for any set of parameters that characterize the model.We exploit the grassmannian nature of the variables involved in the path integral expression of the grand canonical partition function for self--interacting fermionic models to show, in one-space dimension, a general relation among the terms of it expansion in the high temperature limit and a combination of co-factors of a suitable matrix with commuting entries. As an application, we apply this framework to calculate the exact coefficients, up to order β^3, of the expansion of the grand canonical partition function for the Hubbard model in d=(1+1) in the high temperature limit. The results are valid for any set of parameters that characterize the model.

arXiv:cond-mat/9607171Jul 24, 19960 citations

{\mathit{i}}_{13/2}

pairing model for which the exact canonical and grand canonical results can be obtained. It is found that both number projection methods fail to predict the position or the height of the peak in the heat capacity due to errors in the approximation to the grand partition function, even though the path integral approximation is very good.