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Statistic properties of fermi gas in a strong magnetic field

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Chinese Physics B 2010年第3期19卷 108-111页

作者：门福殿范召兰 College of Physics Science and Technology China University of Petroleum(East China)

Based on the thermodynamic potential function of fermi gas in a strong magnetic field, using the thermodynamics method, the integrated analytical expressions of thermodynamic quantities of the system at low temperatures are derived, and the effects of the magnetic field on the statistic properties of the system are analysed. It is shown that, as long as the temperature is not zero, the effects of the magnetic field on the thermodynamic quantities of the system contain both oscillatory and non-oscillatory parts. For the non-oscillatory part, compared with the situation of fermi gas in a weak magnetic field, the influence of the magnetic field on the thermodynamic quantities is not exactly the same. For the oscillatory part, the period and amplitude of the oscillation are all related to the magnetic field. Due to the oscillation, the chemical potential may be greater than Ferim energy of the system, but the oscillation does not affect the thermodynamic stability of the system.

关键词： strong magnetic field fermi gas statistic property

Ground State Energy of One-Dimensional δ-Function Interacting Bose and fermi gas

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Chinese Physics Letters 2010年第8期27卷 23-26页

作者：尤亦庄 Institute for Advanced Study Tsinghua University Beijing 100084

The ground state energy curves of one-dimensional ＆function interacting bose and fermi gas are fitted with simple algebraic approximations according to their asymptotic behaviors.

关键词： Dimensional Interacting Bose fermi gas

Thermodynamic stability of a weakly interacting fermi gas trapped in a harmonic potential

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Chinese Physics B 2008年第9期17卷 3236-3240页

作者：门福殿刘慧朱后禹 College of Physics Science and Technology China University of Petroleum (East China) College of Science Anhui Science and Technology University

Based on the theoretical results derived from pseudopotential method and local approximation, this paper studies the thermodynamic stability of a weakly interacting fermi gas trapped in a harmonic potential by using analytical method of thermodynamics. The effects of the interparticle interactions as well as external potential on the thermodynamic stability of the system are discussed. It is shown that the system is stable as for the complete average, but as for local parts, the system is unstable anywhere. This instability shows that the stability conditions of mechanics cannot be satisfied anywhere, and the stability conditions of thermostatics cannot be satisfied somewhere. In addition, the interactions and external potential have direct effects on the local stability of the system.

关键词： fermi gas interaction stability

Relativistic thermodynamic properties of a weakly interacting fermi gas in a weak magnetic field

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Chinese Physics B 2009年第7期18卷 2649-2653页

作者：门福殿刘慧范召兰朱后禹 College of Physics Science and Technology China University of Petroleum(East China) College of Science Anhui Science and Technology University

This paper derives the analytical expression of free energy for a weakly interacting fermi gas in a weak magnetic field, by using the methods of quantum statistics as well as considering the relativistic effect. Based on the derived expression, the thermodynamic properties of the system at both high and low temperatures are given and the relativistic effect on the properties of the system is discussed. It shows that, in comparison with a nonrelativistic situation, the relativistic effect changes the influence of temperature on the thermodynamic properties of the system at high temperatures, and changes the influence of particle-number density on them at extremely low temperature. But the relativistic effect does not change the influence of the magnetic field and inter-particle interactions on the thermodynamic properties of the system at both high and extremely low temperatures.

关键词： fermi gas relativistic effect thermodynamic property

Many-body theories of density response for a strongly correlated fermi gas

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Frontiers of physics 2012年第1期7卷 98-108页

作者： Hui Hu (1) 1. ARC Centre of Excellence for Quantum-Atom Optics Centre for Atom Optics and Ultrafast Spectroscopy Swinburne University of Technology Melbourne 3122 Australia

Recent breakthroughs in the creation of ultracold atomic gases in the laboratory have ushered in major changes in physical science. Many novel experiments are now possible, with an unprecedented control of interaction, geometry and purity. Quantum many-body theory is facing severe challenges in quantitatively understanding new experimental results. Here, we review some recently developed theoretical techniques that provide successful predictions for density response of a strongly correlated atomic fermi gas. These include the strong-coupling random-phase approximation theory, high- temperature quantum virial expansion, and asymptotically exact Tan relations applicable at large momentum.

关键词： quantum many-body theory fermi gas

Thermal stability conditions of a weakly interacting fermi gas in a weak magnetic field

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Progress in Natural Science:Materials International 2009年第1期19卷 121-124页

作者： Fudian Mena,Hui Liub,Houyu Zhua a College of Physics Science and Technology,China University of Petroleum(East China),Dongying 257061,China b College of Science,Anhui Science and Technology University,Fengyang 233100,China College of Physics Science and Technology China University of Petroleum (East China) Dongying 257061 China College of Science Anhui Science and Technology University Fengyang 233100 China

On the basis of the results derived from pseudopotential method and ensemble theory,thermal stability of a weakly interacting fermi gas in a weak magnetic field is studied by using analytical method of thermodynamics.The exact analytical expressions of stability conditions at different temperatures are given,and the effects of interactions as well as magnetic field on the stability of the system are discussed.It is shown that there is an upperlimit magnetic field for the stability of the system at low temperatures,and there is an attractive dividing value at high temperatures.If attractive interaction is lower than the critical value,the stability of the system has no request for magnetic field,but if attractive interaction is higher than the dividing value,a lower-limit magnetic field exists for the stability of the system.

关键词： fermi gas Interaction Heat capacity Stability

Thermostatistic Properties of the Relativistic q-Deformed Ideal fermi gas at High Temperature

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Wuhan University Journal of Natural Sciences 2010年第1期15卷 57-63页

作者： LIU Hui MEN Fudian LI Yong GUAN Banggui ZHANG Maolian College of Science Anhui Science and Technology University Bengbu 233100 Anhui China College of Physics Science and Technology China University of Petroleum (East China) Dongying 257061 Shandong China

The q-deformed fermi-Dirac distribution is used to study the high-temperature（T TF） ∨behavior of a relativistic q-deformed ideal fermi gas. The effects of the q-deformation and relativity on the properties of the system are discussed,and then,the example of the neutrinos near the surface of the earth is used to calculate approximately. It shows that the q-deformation increases the total energy but decreases the chemical potential and heat capacity,whereas mc 2 ε F0increases the chemical potential and total energy but decreases the heat capacity（ ε F0is the fermi energy of ultrarelativistic undeformed fermi gas） . The larger the deformation parameter q and the value of mc 2 ε F0are,the more remarkable the effects of them on the thermostatistic properties will be. However,the effects of both q-deformation and relativity become weak with increasing temperature. When the temperature T →∞,the thermostatistic properties of the system are reduced to those of ordinary Boltzmann gases and independent of q and relativity effect completely,which implies that the q-deformation is a pure quantum effect.

关键词： thermostatistic property q-deformation relativity fermi gas

Thermodynamic properties of two-dimensional charged spin-1/2 fermi gases

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Chinese Physics B 2022年第6期31卷 254-259页

作者：杨家营刘旭秦吉红郭怀明 Department of Physics University of Science and Technology BeijingBeijing 100083China Institute of Theoretical Physics University of Science and Technology BeijingBeijing 100083China Department of Physics Beihang UniversityBeijing 100191China

Based on the mean-field theory,we investigate the thermodynamic properties of the two-dimensional(2D)charged spin-1/2 fermi gas.Lande′factor g is introduced to measure the strength of the paramagnetic effect.There is a competition between diamagnetism and paramagnetism in the system.The larger the Lande′factor,the smaller the entropy and specific heat.Diamagnetism tends to increase the entropy,while paramagnetism leads to the decrease of the entropy.We find that there exists a critical value of Lande′factor for the transition point due to the competition.The entropy of the system increases with the magnetic field when g0.58,the entropy first decreases with the magnetic field,then reaches a minimum value,and finally increases again.Both the entropy and specific heat increase with the temperature,and no phase transition occurs.The specific heat tends to a constant value at the hightemperature limit,and it approaches to zero at very low temperatures,which have been proved by the analytical calculation.

关键词： fermi gas entropy specific heat Landéfactor

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

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Chinese Physics B 2006年第12期15卷 2856-2860页

作者：门福殿刘慧 College of Physics Science and Technology China University of Petroleum (East China) Dongying 257061 China

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 （αn-k 4εF/3）（n and εF denote the particle-number density and the fermi energy respectively, α = 4πah^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 （αn ＋ 4εF/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 ｜α｜ 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.

关键词： fermi gas interaction instability conditions