Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

DEStech Transactions on Materials Science and Engineering

Research on the Thermodynamic Property of Weakly Interacting Fermi Gases Through N-E-V Distribution and Pseudopotential Method

Heling Li, Juanjuan Wang, Bin Yang, Hongjun Shen

Published May 31, 2017• 0 citations
Publisher

Abstract

As the experiments of quantum system are conducted in the external field where the volume, energy and particle number are variable, the thermodynamic property of weakly interacting Fermi system is studied in this paper through the statistical distribution (N-E-V distribution) of a completely open system where the volume, energy and particle number are variable. Firstly, analytical expressions of internal energy, the equation of state, entropy and heat capacity expressed by Fermi integral are worked out. On that basis, the analytical expression and results of numerical calculation of the above thermodynamic quantities in extremely low temperature conditions can be known. Then, comparison between the calculations of N-E-V distribution and pseudopotential method (the volume and particle number remain the same) is drawn. The results show that the calculation of N-E-V distribution always makes up for the deviation of that of pseudopotential method. Besides, the most special thing about the calculation derived from N-E-V distribution is that the temperature variation curve of internal energy and that in the ideal Fermi system intersect. The characteristics of energy transfer between “attractive force” and “repulsive force” at the intersection temperature tc, which indicates that there is a phase transition. The intersection temperature does not change with the scattering length a (a0 repulsive force). Moreover, the intersection temperature of all weakly interacting Fermi system is 0.184 times as large as Fermi temperature, which is within the range of temperature for BEC and BCS phase transition and BEC-BCS crossover.

DOI
10.12783/dtmse/smne2016/10567

Related papers

Investigation of thermodynamic properties of weakly interacting Fermi gas in weakly magnetic field by using the N-E-V distribution and pseudopotential method

Heling Li, Juanjuan Wang, Bin Yang +1 more

Based on the fact that most of low temperature experiments of quantum systems are explored in an external field on condition that the particle numbers, volumes and energies of systems may be changed, the thermodynamic properties of weakly interacting Fermi systems in weak magnetic field are studied by using the statistical distribution of the completely open system with variable particle number, volume, and energy (N-E-V distribution). Firstly, the analytical expressions of internal energy and heat capacity, which are in the Fermi integral form, are obtained in the general case, and the analytical expressions and numerical results of energy and heat capacity are given under the extreme condition of supper-low temperature. The calculation results by the N-E-V distribution (with particle number density being variable) are compared with those by a pseudopotential method (with particle number density being unchanged). It can be found that the deviations of the internal energy and heat capacity calculated by the two different methods are very small, and the N-E-V distribution method can partially compensate for the error caused by the pseudo potential method. The most interesting point of the results obtained by the N-E-V distribution method is that there is a phase transition temperature in the weakly interacting Fermi system in weak magnetic field under the low temperature condition. The phase transition temperature is just in the range where occur the Fermi systems, Bose-Einstein condensation (BEC), Bardeen-Cooper-Schrieffer (BCS) phase transition, and BEC-BCS crossover, and does not vary with strength nor characteristic (attraction or repulsion) of the weak interaction, but it decreases with the strengthening of the external magnetic. When there is no external magnetic, the phase transition temperature is highest (more than 0.184 times Fermi temperature).

Acta Physica Sinica•Jan 1, 2015•1 citation

Thermodynamic properties of a weakly interacting Fermi gas in a strong magnetic field

Men Fu-Dian, Wang Bing-Fu, He Xiao-Gang +1 more

Based on the pseudopotential method and the local-density approximation, the thermodynamic properties of a weakly interacting Fermi gas in a strong magnetic filed are studied, the integrated analytical expressions of thermodynamic quantities of the system are derived, and the effects of magnetic field as well as interparticle interactions on the thermodynamic properties of the system are analyzed. It is shown that at both high and low temperatures, magnetic field may adjust the effects of interacting. At low temperatures, magnetic field can lower the chemical potential, total energy and heat capacity of the system compared with the situation of Fermi gas in the absence of the magnetic field. The repulsive interactions may increase the chemical potential, but reduce the total energy and heat capacity of the system compared with the situation of non-interacting Fermi gas. At high temperatures, magnetic field as well as repulsive interactions can reduce the total energy and increase heat capacity of the system, moreover, strong magnetic field may change the effects of interaction on the total energy and the heat capacity of the system.

Acta Physica Sinica•Jan 1, 2011•2 citations

Thermodynamic properties of Fermi gas under generalized uncertainty principle

Heling Li, Juanjuan Wang, Bin Yang +2 more

When taking into account the generalized uncertainty principle in statistical physics, the density of states must make a correction, which causes all the results of traditional statistical physics to have different degrees of correction. In high-energy or high-temperature conditions, this amendment can subvert the traditional concept and there are also some certain amendments at low temperatures. In this paper we study the thermodynamic properties of the ideal and weakly interacting Fermi gas in low temperature conditions when the generalized uncertainty principle is taken into account. Firstly, analytical expressions of chemical potential, internal energy and heat capacity at constant volume of ideal or weakly interacting Fermi gas are given. Then the properties of copper electron gas are computed as an example, showing that when the generalized uncertainty principle is taken into account the chemical potential, Fermi energy and the ground state energy increase with the increase of temperature, while the heat capacity decreases. When the temperature is lower than 0.3 times TF0, the internal energy increases with the increase of temperature, but becomes decreased when temperature is high than 0.3 times TF0. These amendments are mostly dependent on particle density, which becomes bigger and bigger with particle density increasing.

Acta Physica Sinica•Jan 1, 2015•2 citations

Thermodynamic properties of a weakly interacting Fermi gas

Guozhen Su, Lixuan Chen, 厦门大学物理系，厦门 361005

The analytical expressions of chemical potential, total energy and heat capacity at a constant volume for a weakly interacting Fermi gas in the absence of external potential are derived by using “pseudopotential” method. Based on the derived expressions, the thermodynamic properties of a weakly interacting Fermi gas trapped in a harmonic potential are studied under the local-density approximation. The effects of interparticle interactions on the properties of the systems are discussed.

Acta Physica Sinica•Jan 1, 2004•13 citations

Effects of a finite number of particles on a weakly interacting Fermi gas in weak magnetic field

LV Lin

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.

Journal of Atomic and Molecular Physics•Jan 1, 2007•0 citations

Thermodynamic properties of a weakly interacting Fermi gas in weak magnetic field

Men Fu-Dian, 中国石油大学(华东)物理科学与技术学院，东营 257061

The analytical expressions of internal energy, chemical potential and heat capacity of the little parameter r for a weakly interacting Fermi gas in weak magnetic field are derived by using “pseudopotential" method and ensemble theory. Based on the derived expressions, the thermodynamic properties of a weakly interacting Fermi gas in weak magnetic field at both high and low temperatures are given. The effects of magnetic field and interparticle interactions on the thermodynamic properties are discussed. The difference in the effects of magnetic trap and three-dimensional harmonic trap on the properties of the system and their reasons are analyzed.

Acta Physica Sinica•Jan 1, 2006•10 citations
As the experiments of quantum system are conducted in the external field where the volume, energy and particle number are variable, the thermodynamic property of weakly interacting Fermi system is studied in this paper through the statistical distribution (N-E-V distribution) of a completely open system where the volume, energy and particle number are variable. Firstly, analytical expressions of internal energy, the equation of state, entropy and heat capacity expressed by Fermi integral are worked out. On that basis, the analytical expression and results of numerical calculation of the above thermodynamic quantities in extremely low temperature conditions can be known. Then, comparison between the calculations of N-E-V distribution and pseudopotential method (the volume and particle number remain the same) is drawn. The results show that the calculation of N-E-V distribution always makes up for the deviation of that of pseudopotential method. Besides, the most special thing about the calculation derived from N-E-V distribution is that the temperature variation curve of internal energy and that in the ideal Fermi system intersect. The characteristics of energy transfer between “attractive force” and “repulsive force” at the intersection temperature tc, which indicates that there is a phase transition. The intersection temperature does not change with the scattering length a (a0 repulsive force). Moreover, the intersection temperature of all weakly interacting Fermi system is 0.184 times as large as Fermi temperature, which is within the range of temperature for BEC and BCS phase transition and BEC-BCS crossover.
Based on the fact that most of low temperature experiments of quantum systems are explored in an external field on condition that the particle numbers, volumes and energies of systems may be changed, the thermodynamic properties of weakly interacting Fermi systems in weak magnetic field are studied by using the statistical distribution of the completely open system with variable particle number, volume, and energy (N-E-V distribution). Firstly, the analytical expressions of internal energy and heat capacity, which are in the Fermi integral form, are obtained in the general case, and the analytical expressions and numerical results of energy and heat capacity are given under the extreme condition of supper-low temperature. The calculation results by the N-E-V distribution (with particle number density being variable) are compared with those by a pseudopotential method (with particle number density being unchanged). It can be found that the deviations of the internal energy and heat capacity calculated by the two different methods are very small, and the N-E-V distribution method can partially compensate for the error caused by the pseudo potential method. The most interesting point of the results obtained by the N-E-V distribution method is that there is a phase transition temperature in the weakly interacting Fermi system in weak magnetic field under the low temperature condition. The phase transition temperature is just in the range where occur the Fermi systems, Bose-Einstein condensation (BEC), Bardeen-Cooper-Schrieffer (BCS) phase transition, and BEC-BCS crossover, and does not vary with strength nor characteristic (attraction or repulsion) of the weak interaction, but it decreases with the strengthening of the external magnetic. When there is no external magnetic, the phase transition temperature is highest (more than 0.184 times Fermi temperature).
Based on the pseudopotential method and the local-density approximation, the thermodynamic properties of a weakly interacting Fermi gas in a strong magnetic filed are studied, the integrated analytical expressions of thermodynamic quantities of the system are derived, and the effects of magnetic field as well as interparticle interactions on the thermodynamic properties of the system are analyzed. It is shown that at both high and low temperatures, magnetic field may adjust the effects of interacting. At low temperatures, magnetic field can lower the chemical potential, total energy and heat capacity of the system compared with the situation of Fermi gas in the absence of the magnetic field. The repulsive interactions may increase the chemical potential, but reduce the total energy and heat capacity of the system compared with the situation of non-interacting Fermi gas. At high temperatures, magnetic field as well as repulsive interactions can reduce the total energy and increase heat capacity of the system, moreover, strong magnetic field may change the effects of interaction on the total energy and the heat capacity of the system.
When taking into account the generalized uncertainty principle in statistical physics, the density of states must make a correction, which causes all the results of traditional statistical physics to have different degrees of correction. In high-energy or high-temperature conditions, this amendment can subvert the traditional concept and there are also some certain amendments at low temperatures. In this paper we study the thermodynamic properties of the ideal and weakly interacting Fermi gas in low temperature conditions when the generalized uncertainty principle is taken into account. Firstly, analytical expressions of chemical potential, internal energy and heat capacity at constant volume of ideal or weakly interacting Fermi gas are given. Then the properties of copper electron gas are computed as an example, showing that when the generalized uncertainty principle is taken into account the chemical potential, Fermi energy and the ground state energy increase with the increase of temperature, while the heat capacity decreases. When the temperature is lower than 0.3 times TF0, the internal energy increases with the increase of temperature, but becomes decreased when temperature is high than 0.3 times TF0. These amendments are mostly dependent on particle density, which becomes bigger and bigger with particle density increasing.
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.
The analytical expressions of internal energy, chemical potential and heat capacity of the little parameter r for a weakly interacting Fermi gas in weak magnetic field are derived by using “pseudopotential" method and ensemble theory. Based on the derived expressions, the thermodynamic properties of a weakly interacting Fermi gas in weak magnetic field at both high and low temperatures are given. The effects of magnetic field and interparticle interactions on the thermodynamic properties are discussed. The difference in the effects of magnetic trap and three-dimensional harmonic trap on the properties of the system and their reasons are analyzed.