The Research And Application Of Thermodynamic Properties Of Anyon Gas In Any Dimension

Quantum statistical mechanics has been widely used and made great achieve-ments.Recently,physicists developed fractional exclusion statistics by generalizing the conventional quantum statistics mechanics,where anyons with different quan-tum statistics from fermions and bosons are proposed.It has also been noticed that in the non-relativistic ideal Fermi gas a curious "hump" may develop in the chemi-cal potential for low dimensionality.Therefore it is of great interest to explore the thermodynamic behaviour of anyon in low dimension.In the thesis,we explore the thermodynamic properties of anyon system with fractional exclusion statistics in any dimension,study the simple application of anyon system in physics,and demonstrate the relation of physical quantities and statistical parameters.So far,physicists have only calculated the thermodynamic quantities of anyon system with non-relativistic(?=p2/2m),ultrarelativistic dispersion relation(?=cp)and trapped by harmonic potential in any dimension.The focus of this paper is to calculate and derive the thermodynamic quantities of anyon system with Gentile statistics,Haldane fraction exclusion statistics and polychronakos fraction statistics in general dispersion relations(?=D?|p|?,1???2)or trapped by isotropic potential(?=D?|p|?+U0(r/r0)t)in any dimension,and to carry out numerical sim-ulation.We also explore the simply application of anyon system.The main content and results of this paper are as follows:1.The thermodynamic quantities of anyon system with three kinds of fraction-al exclusion statistics in any dimension,such as particle number,internal energy,chemical potential,pressure,entropy and isothermal compressibility,which satisfy the general dispersion relation or trapped by isotropic potential,are investigated with analytical derivation and numerical simulation.We find that the thermody-namic quantities of particles satisfying the general dispersion relation and trapped by isotropic potential in any dimension can be identified by the same index s,which is expressed respectively d/??d/?+d/t.2.When s<1 1 the "hump" is observed in the chemical potential of anyon system with Gentile statistics,Haldane fraction exclusion statistics and polychron-akos fraction statistics at low temperature,and the "hump" goes up as statistical parameters increases when the temperature is constant.And the chemical potential and internal energy of anyon system still depend on the statistical parameters at high temperature.The internal energy of a single particle becomes large with the increase of statistical parameters when s and T.are constant,or increase of s when the statistical parameters and temperature are constant.3.When the temperature is constant,the entropy function of a single particle of anyon system is related to s with the variation trend of statistical parameters.The entropy of a single particle decreases with statistical parameters when s<1,increases with statistical parameters when s>1.While the entropy of a single particle is hardly affected by statistical parameters at s=1.When the statistical parameters and temperature are constant,the entropy of a single particle increases with s.4.When the anyon system satisfies the general dispersion relation or is trapped by isotropic potential,a maximum Joule-Thomson transition temperature exists in ideal anyon system with Gentile statistics and Haldane fraction exclusion statistics,which is similar to that of non-ideal gas.However,the Joule-Thomson coefficient of anyon system with Polychronakos fraction statistics is similar to that of an ideal quantum system(ideal boson system and Fermi system).When 0<l<0.5,the Joule-Thomson coefficient of anyon system becomes smaller with the increase of tem-perature and is always positive,which is similar to the Joule-Thomson coeficient of ideal Bose gas.When 0.5<k<1,the Joule-Thomson coefficient of anyon system increases with temperature and is always negative,which is similar to the Joule-Thomson coefficient of ideal Fermi gas.5.The agreements between the theoretical curves and the experimental data show that the statistics parameters of fraction exclusion statistics can be capable of describing the strong interaction of unitary Fermi gas.Furthermore,we find that the viscosity coefficient and the ratio of thermal conductivity to electrical conductivity of anyon system with three kinds of fraction exclusion statistics all depend on statistical parameters and increase with statistical parameters at a certain temperature.