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Physics Letters A

Effects of a finite number of particles on the thermodynamic properties of a noninteracting trapped Fermi gas

Guozhen Su, Lixuan Chen, Jincan Chen

Published Apr 30, 2004• 18 citations
Publisher
DOI
10.1016/j.physleta.2004.04.038

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The partition function of system with finite number of particles is derived is derived by using partition function of a weakly interacting Fermi gas trapped in weak magnetic field.Based on the derived expressions,the analytical expressions of thermodynamic quantities of a weakly interacting Fermi gas for finite particle number are solved by using statistical average method and the thermodynamic properties under different temperature conditions are given.It is shown that each thermodynamic quantity has a correctional term due to effects of a finite number of particles.The particle number has a direct effect on correction of chemical potential but has no direct effects on corrections of total energy and heat capacity except T=0.Furthermore,effects of a finite number of particles always reduce chemical potential,thereby zero point of chemical potential shifts towards low temperatures.The increase of particle number weakens the effect,but the repulsive interactions between particles strengthen the effect.

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At zero-temperature and finite-temperature, the thermodynamic properties of finite unitary Fermi gas in a three-dimensional harmonic trap are investigated by using fractional exclusion statistics, and the results are compared with those of the system which satisfies the thermodynamic limit. At zero-temperature, Fermi energy and average energy of per particle increase with the increase of the number of particles for finite unitary Fermi gas, and their limits are the corresponding parameters of the system which satisfy thermodynamic limits. Fermi energy and average energy of per particle each have a maximum value changing with the boundary of the potential well. For the finite-temperature trapped unitary Fermi system, when the number of particles is certain the average energy of per particle, average entropy of per particle, average heat capacity of per particle each have a characteristic temperature, respectively, when the temperature is equal to the characteristic temperature of the physical parameter, the corresponding parameters for the finite system and the thermodynamic limit system are equal, when the temperature is lower (or higher) than the characteristic temperature of parameter, the physical parameter of the finite system will be greater (or less) than the corresponding parameter of the thermodynamic limit system. The characteristic temperature has particle number effect and boundary effect. When the temperature is determined, the average energy of per particle, average entropy of per particle and average heat capacity of per particle each have a characteristic number of particles, respectively, when the number of particles is equal to the characteristic number of particles for physical parameter, the corresponding parameters for the finite system and the thermodynamic limit system are equal, when the number of particles is less (or more) than the characteristic number of particles for corresponding parameter, the corresponding parameter of the finite system will be less (or larger) than the thermodynamic limit of system.

Acta Physica Sinica•Jan 1, 2016•2 citations
The effects of a finite number of particles on the thermodynamic properties of ideal Bose and Fermi gases trapped in any-dimensional harmonic potential are investigated. The orders of relative corrections to the thermodynamic quantities due to the finite number of particles are estimated in different situations. The results obtained for the two trapped quantum gases are compared, and consequently, it is shown that the finite-particle-number effects for the condensed Bose gas (a Bose gas with Bose–Einstein Condensation (BEC) occurring in the system) are much more significant than those for the Fermi gas and normal Bose gas (a Bose gas without BEC).
The partition function of system with finite number of particles is derived is derived by using partition function of a weakly interacting Fermi gas trapped in weak magnetic field.Based on the derived expressions,the analytical expressions of thermodynamic quantities of a weakly interacting Fermi gas for finite particle number are solved by using statistical average method and the thermodynamic properties under different temperature conditions are given.It is shown that each thermodynamic quantity has a correctional term due to effects of a finite number of particles.The particle number has a direct effect on correction of chemical potential but has no direct effects on corrections of total energy and heat capacity except T=0.Furthermore,effects of a finite number of particles always reduce chemical potential,thereby zero point of chemical potential shifts towards low temperatures.The increase of particle number weakens the effect,but the repulsive interactions between particles strengthen the effect.
At zero-temperature and finite-temperature, the thermodynamic properties of finite unitary Fermi gas in a three-dimensional harmonic trap are investigated by using fractional exclusion statistics, and the results are compared with those of the system which satisfies the thermodynamic limit. At zero-temperature, Fermi energy and average energy of per particle increase with the increase of the number of particles for finite unitary Fermi gas, and their limits are the corresponding parameters of the system which satisfy thermodynamic limits. Fermi energy and average energy of per particle each have a maximum value changing with the boundary of the potential well. For the finite-temperature trapped unitary Fermi system, when the number of particles is certain the average energy of per particle, average entropy of per particle, average heat capacity of per particle each have a characteristic temperature, respectively, when the temperature is equal to the characteristic temperature of the physical parameter, the corresponding parameters for the finite system and the thermodynamic limit system are equal, when the temperature is lower (or higher) than the characteristic temperature of parameter, the physical parameter of the finite system will be greater (or less) than the corresponding parameter of the thermodynamic limit system. The characteristic temperature has particle number effect and boundary effect. When the temperature is determined, the average energy of per particle, average entropy of per particle and average heat capacity of per particle each have a characteristic number of particles, respectively, when the number of particles is equal to the characteristic number of particles for physical parameter, the corresponding parameters for the finite system and the thermodynamic limit system are equal, when the number of particles is less (or more) than the characteristic number of particles for corresponding parameter, the corresponding parameter of the finite system will be less (or larger) than the thermodynamic limit of system.