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Modern Physics Letters B

STATISTICAL PROPERTIES OF A TRAPPED RELATIVISTIC FERMI GAS WITH PAIR PRODUCTION

Guozhen Su, LIWEI CHEN, Jincan Chen

Published Sep 11, 2013• 2 citations
Publisher

Abstract

Statistical properties of an ideal gas of relativistic fermions trapped in a D-dimensional power-law potential are studied, in which the effect of particle–antiparticle pair production is taken into account. It is shown that the relativistic effect is considerable even at very low temperatures for the system with Fermi energy comparable with the rest energy of a particle. In contrast, the effect of pair production is significant at high temperatures, but negligible at low temperatures. Moreover, it is found that the pair production results in several novel characteristics, such as the asymptotic behavior of chemical potential and rapid increase of heat capacity in the high temperature region.

DOI
10.1142/s0217984913501777

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Statistical properties of an ideal gas of relativistic fermions trapped in a D-dimensional power-law potential are studied, in which the effect of particle–antiparticle pair production is taken into account. It is shown that the relativistic effect is considerable even at very low temperatures for the system with Fermi energy comparable with the rest energy of a particle. In contrast, the effect of pair production is significant at high temperatures, but negligible at low temperatures. Moreover, it is found that the pair production results in several novel characteristics, such as the asymptotic behavior of chemical potential and rapid increase of heat capacity in the high temperature region.
An ideal gas of relativistic bosons trapped in a D -dimensional power-law potential is explored, where the possibility of particle–antiparticle pair production is taken into account. Expressions for several important parameters, such as the critical temperature of Bose–Einstein condensation (BEC), ground-state fraction and heat capacity, are analytically derived and used to discuss the relevant properties of the system. An important parameter χ is introduced to mark the extent of the relativistic effects on the characteristics of BEC. It is found that the correction of the critical temperature due to the relativistic effects is considerable for the system with a large parameter χ. It is more important to show that the pair production may lead to several novel characteristics for a relativistic Bose gas, such as the high temperature BEC, the rapid increase of the heat capacity at high temperatures and the disappearance of the anomaly of the heat capacity at the critical temperature in the ultrarelativistic limit.
Based on the semiclassical(Thomas-Fermi) approximation,the macrocanonical partition function and macrocanonical potential of a relativistic Fermi gas in a general external potential in any dimensional space are studied.The general analytical expressions of the total particle number N,total energy U and heat capacity C have been derived with thermodynamic fundamental equations,where N,U and C are expressed by the modified Bessel function.Moreover,the analytical expressions of the total energy,chemical potential and heat capacity in the high-and low-temperature approximations are given.From these results,how the characteristics of the Fermi gas depend on various factors is discussed.
The effects of low dimensionality on the thermodynamics of a Fermi gas trapped by isotropic power-law potentials are analyzed. Particular attention is given to different characteristic temperatures that emerge, at low dimensionality, in the thermodynamic functions of state and in the thermodynamic susceptibilities (isothermal compressibility and specific heat). An energy-entropy argument that physically favors the relevance of one of these characteristic temperatures, namely, the nonvanishing temperature at which the chemical potential reaches the Fermi energy value, is presented. Such an argument allows interpreting the nonmonotonic dependence of the chemical potential on temperature, as an indicator of the appearance of a thermodynamic regime, where the equilibrium states of a trapped Fermi gas are characterized by larger fluctuations in energy and particle density as is revealed in the corresponding thermodynamics susceptibilities.
Based on the methods of quantum statistics, by considering relativistic correction of single particle and introducing the nonrelativistic free energy of the system of spinless and free fermions,the free energy for Fermi gas in a weak magnetic field is derived, thereout the analytical expressions of thermodynamic quantities of the system under various temperature condtions are given, the effects of relativistic correction on the properties of the nonrelativistic system are exhibited particular and concrete, and the mechanism of the effects is analysed. Compared with those of nonrelativistic situation, it is shown that the effects of relativistic correction always reduce chemical potential. The effects of relativistic correction decrease the total energy and heat capacity at low temperatures, while increase them at high temperatures. The changes of the total energy and heat capacity (not include the low-temperature heat capacity ) are proportional to the square of magnetic field.
Using the methods of numerical simulation and quantum statistics, based on the thermodynamic quantities of Fermi gas trapped in a general external potential, we studied the thermodynamic properties of a relativistic Fermi gas trapped in hard-sphere potential, gave the analytical expressions of the energy and heat capacity of the relativistic Fermi system, and analyzed the influence of the relativistic effect on the energy and heat capacity. The results showed the energy and heat capacity of the relativistic Fermi system is larger than those of the nonrelativistic case. The larger the relativistic eigenvalue, the lower the change temperature of heat capacity. As the temperature rises, the larger the relativistic eigenvalue, the greater the energy.