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

Acta Physica Sinica

Stability of a weakly interacting Fermi gas in a strong magnetic field

Men Fu-Dian, Tian Qing-Song, Chen Xin-Long

Published Jan 1, 2014• 0 citations
Publisher

Abstract

Using the quantum statistical theory, the stability of a weakly interacting Fermi gas trapped in a strong magnetic field is investigated, the expression of stability condition is given, and the mechanisms of influences of interparticle interaction and magnetic field on the stability are analyzed. The results show that repulsive interaction will increase both the chemical potential and the space domain needed for system stability. But, the increasing of magnetic field strength will reduce the space domain needed for the system stability, and lower the stability of the particle number density distribution.

DOI
10.7498/aps.63.120504

Related papers

The instability conditions of a weakly interacting Fermi gas trapped in weak magnetic field

Men Fu-Dian, Liu Hui

In this paper the analytical expression of free energy expressed by small parameter r of a weakly interacting Fermi gas trapped in weak magnetic field is derived by using `the maximum approximation' method and the ensemble theory. Based on the derived expression, the exact instability conditions of a weakly interacting Fermi gas trapped in weak magnetic field at both high and low temperatures are given. From the instability conditions we get the following two results. (1) At the whole low-temperature extent, whether the interactions are repulsive or attractive with (α n +4ε F /3) ( n and ε F denote the particle-number density and the Fermi energy respectively, α = 4π a ℏ 2 / m , and a is s-wave scattering length) positive, there is a lower-limit magnetic field of instability; in addition, there is an upper-limit magnetic field for the system of attractive interactions with (α n +4ε F /3) negative. (2) At the whole high-temperature extent, the system with repulsive interactions is always stable, but for the system with attractive interactions, the greater the scattering length of attractive interactions | a | is, the stronger the magnetic field is and the larger the particle-number density is, the bigger the possibility of instability in the system will be.

Chinese Physics•Nov 2, 2006•5 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

The stability and paramagnetism of Fermi gas in a strong magnetic field

Men Fu-Dian, Wang Hai-Tang, He Xiao-Gang

By using theoretical analysis and numerical simulation, the stability and the paramagnetism of Fermi gas in a strong magnetic field at low temperatures are studied, and the influences of temperature and magnetic field on the stability and susceptibility of the system are analyzed. The results show that the strong magnetic field causes variation of a system stability, and such a change relates to temperature. While the effects of temperature on stability and susceptibility are relevant to the chemical potential (i.e. the particle number density) of free gas. When the chemical potential is even, the magnetic field weakens the stability of the system, and the increasing of temperature leads to the reduction in the susceptibility of the system. When the chemical potential is odd, the magnetic field strengthens the stability of the system, while the increasing of temperature can increase the susceptibility of the system. With temperature increasing, the effect of the magnetic field on the stability is weakened. With magnetic field increasing, the change of the stability of the system becomes oscillatory, and the oscillation center of the susceptibility shifts down.

Acta Physica Sinica•Jan 1, 2012•0 citations

Relativity stability of quantum gas in a weak magnetic field

Men Fu-Dian, Liu Hui, Fan Zhao-Lan +1 more

Based on the analytical expression of relativistic free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the method of quantum statistics, the stability conditions of the system at both high and low temperatures are given, and the effects of magnetic field and interparticle interactions on the stability of the system are analysed. It is shown that at high temperatures, the stability conditions of the system are completely the same, no matter whether it is the ultrarelativistic case or nonrelativistic case. At extremely low temperatures, the mechanical stability conditions of the system show a similar rule through a comparison between the ultrarelativistic case and nonrelativistic case. At the same time, thermal stability of a relativistic Bose gas in a weak magnetic field is discussed, and the influence of the effect of relativity on the thermal stability of the system is investigated.

Chinese Physics B•Sep 1, 2009•1 citation

Relativisticstability of interacting Fermi gas in a strong magnetic field

Wang Lie

By means of the single particle energy spectrum of weak interaction between fermions and Poisson formula,the thermodynamic potential function of relativistic Fermi gas in a strong magnetic field is derived.Based on this,we obtained the criterion of stability for the system.The results show that the mechanics stability of a Fermi gas with weak interacting is influenced by the interacting.While the magnetic field is able to regulate the influence and the relativistic effect has almost no effect on it.

Journal of Atomic and Molecular Physics•Jan 1, 2013•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
Using the quantum statistical theory, the stability of a weakly interacting Fermi gas trapped in a strong magnetic field is investigated, the expression of stability condition is given, and the mechanisms of influences of interparticle interaction and magnetic field on the stability are analyzed. The results show that repulsive interaction will increase both the chemical potential and the space domain needed for system stability. But, the increasing of magnetic field strength will reduce the space domain needed for the system stability, and lower the stability of the particle number density distribution.
In this paper the analytical expression of free energy expressed by small parameter r of a weakly interacting Fermi gas trapped in weak magnetic field is derived by using `the maximum approximation' method and the ensemble theory. Based on the derived expression, the exact instability conditions of a weakly interacting Fermi gas trapped in weak magnetic field at both high and low temperatures are given. From the instability conditions we get the following two results. (1) At the whole low-temperature extent, whether the interactions are repulsive or attractive with (α n +4ε F /3) ( n and ε F denote the particle-number density and the Fermi energy respectively, α = 4π a ℏ 2 / m , and a is s-wave scattering length) positive, there is a lower-limit magnetic field of instability; in addition, there is an upper-limit magnetic field for the system of attractive interactions with (α n +4ε F /3) negative. (2) At the whole high-temperature extent, the system with repulsive interactions is always stable, but for the system with attractive interactions, the greater the scattering length of attractive interactions | a | is, the stronger the magnetic field is and the larger the particle-number density is, the bigger the possibility of instability in the system will be.
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.
By using theoretical analysis and numerical simulation, the stability and the paramagnetism of Fermi gas in a strong magnetic field at low temperatures are studied, and the influences of temperature and magnetic field on the stability and susceptibility of the system are analyzed. The results show that the strong magnetic field causes variation of a system stability, and such a change relates to temperature. While the effects of temperature on stability and susceptibility are relevant to the chemical potential (i.e. the particle number density) of free gas. When the chemical potential is even, the magnetic field weakens the stability of the system, and the increasing of temperature leads to the reduction in the susceptibility of the system. When the chemical potential is odd, the magnetic field strengthens the stability of the system, while the increasing of temperature can increase the susceptibility of the system. With temperature increasing, the effect of the magnetic field on the stability is weakened. With magnetic field increasing, the change of the stability of the system becomes oscillatory, and the oscillation center of the susceptibility shifts down.
Based on the analytical expression of relativistic free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the method of quantum statistics, the stability conditions of the system at both high and low temperatures are given, and the effects of magnetic field and interparticle interactions on the stability of the system are analysed. It is shown that at high temperatures, the stability conditions of the system are completely the same, no matter whether it is the ultrarelativistic case or nonrelativistic case. At extremely low temperatures, the mechanical stability conditions of the system show a similar rule through a comparison between the ultrarelativistic case and nonrelativistic case. At the same time, thermal stability of a relativistic Bose gas in a weak magnetic field is discussed, and the influence of the effect of relativity on the thermal stability of the system is investigated.
By means of the single particle energy spectrum of weak interaction between fermions and Poisson formula,the thermodynamic potential function of relativistic Fermi gas in a strong magnetic field is derived.Based on this,we obtained the criterion of stability for the system.The results show that the mechanics stability of a Fermi gas with weak interacting is influenced by the interacting.While the magnetic field is able to regulate the influence and the relativistic effect has almost no effect on it.
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.