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

Journal of Huangshi Institute of Technology

Study of Chemical Potential of a Confined Fermi Gas with Weak Interaction

Wang Feng

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Schrodinger equation of the weak interaction Fermi gas is educed by using mean field theory-Hartee-Fock theory.The energy Eigenvalue is derived by using separation of variables.Based on the derived expressions,the chemical potential of a confined Fermi gas with weak interaction is studied under numerical solution.The effects of interaction between particles on the chemical potential are discussed.

Related papers

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

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

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

Thermodynamics Properties of Non-idea Quantum Fermi Gases

Wang Wei-bing

The weakly interaction universally exists in actual quantum gases,the analytical expressions of chemical potential,pressure,trophy and heat capacity at a constant volume for actual quantum gases in the absence of external potential are derived using total energy deduced by pseudo potential method,then based on the derived expressions,the effects of inter-particle interaction on the properties of Fermi gas systems are discussed.

Journal of Yantai Vocational College•Jan 1, 2007•0 citations

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

Density profile of the weakly interacting Fermi gas confined in a potential well: Nonzero temperature

J. Oliva

A theory is developed for the low-temperature density profile of a weakly interacting normal Fermi gas confined within an arbitrary potential well. This problem is of interest in connection with magnetically confined spin-aligned atomic deuterium (${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$). The approach used is based on the statement of constancy of the chemical potential in equilibrium. This involves the internal chemical potential, a functional of the density, which we treat within the local-density approximation. We develop an accurate approximate form for the local internal chemical potential: For a given low temperature, it is taken equal to the known forms at low density (classical) and higher density (quantum); for intermediate density we use an appropriate interpolant which smoothly connects the low- and high-density forms. Finite-temperature density profiles are evaluated for the ideal Fermi gas for parameters appropriate to magnetically confined ${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$ for both symmetric linear and quadratic one-dimensionally varying wells. We also evaluate density profiles including the leading-order interparticle interaction effect. For conditions relevant to hypothetical ${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$ at moderate densities this effect is found to be small but measurable.

Physical review. B, Condensed matter•Mar 1, 1989•11 citations
Schrodinger equation of the weak interaction Fermi gas is educed by using mean field theory-Hartee-Fock theory.The energy Eigenvalue is derived by using separation of variables.Based on the derived expressions,the chemical potential of a confined Fermi gas with weak interaction is studied under numerical solution.The effects of interaction between particles on the chemical potential are discussed.
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.
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.
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.
A theory is developed for the low-temperature density profile of a weakly interacting normal Fermi gas confined within an arbitrary potential well. This problem is of interest in connection with magnetically confined spin-aligned atomic deuterium (${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$). The approach used is based on the statement of constancy of the chemical potential in equilibrium. This involves the internal chemical potential, a functional of the density, which we treat within the local-density approximation. We develop an accurate approximate form for the local internal chemical potential: For a given low temperature, it is taken equal to the known forms at low density (classical) and higher density (quantum); for intermediate density we use an appropriate interpolant which smoothly connects the low- and high-density forms. Finite-temperature density profiles are evaluated for the ideal Fermi gas for parameters appropriate to magnetically confined ${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$ for both symmetric linear and quadratic one-dimensionally varying wells. We also evaluate density profiles including the leading-order interparticle interaction effect. For conditions relevant to hypothetical ${\mathrm{D}}_{\mathrm{\ensuremath{\downarrow}}}$ at moderate densities this effect is found to be small but measurable.