On Relativistic Fermi Gas In A Weak Magnetic Field And Weak Interaction

Quantum theory and relativity theory have opened up the opportunities for humans tostudy the world, ranging from the vast universe to the tiny basic components of the substance.The development of these theories continues to promote people’s understanding of the worldand to inspire people to blaze new trails. Based mainly on the two theories, this paper focuseson the thermodynamic quantities and magnetic susceptibility of relativistic Fermi gas in aweak magnetic field and weak interaction.To start with, this paper derives the function expression of thermodynamic potentialsfrom analyzing single-particle energy spectrum relations in the system of a weak magneticfield and weak interaction. Next, the function expressions of thermodynamic quantities andmagnetic permeability of Fermi system under different conditions are also derived fromPoisson’s equation in the weak magnetic field and the modified Bessel. Then, on the basis ofthe above results, numerical simulation is conducted with the use of Matlab software and thusconclusions are drawn as follows.1) The internal energy of Fermi system increases (ordecreases) with the increase (or decrease) of temperature; Only under the condition of lowtemperature does the interaction of particles have influence on the internal energy of Fermisystem, which is not affected by the interaction on other conditions; Only under the conditionof low temperature and weak relativity does magnetic field have effect on the internal energyof Fermi system; The internal energy of weakly relativistic Fermi system has something to dowith the weights of particles while the internal energy of strongly relativistic Fermi systemhas something to do with them only at low temperature.2) The heat capacity at constantvolume of Fermi system increases (or decreases) with the increase (or decrease) oftemperature.3) With the increase (or decrease) of temperature the chemical potential of Fermisystem decreases (or increases), on which the repulsion effect is stronger than that ofattraction effect. Moreover, the changes under the impact display characteristics of their own.4) The three elements(i.e. the internal energy, the heat capacity at constant volume and thechemical potential) of strongly relativistic Fermi system are correspondingly superior to thoseof weakly relativistic Fermi system. In addition, the relativistic effects on the thermodynamic quantities of Fermi gas must be taken into account even when the weight of particles isextremely tiny and the temperature is very low.Finally, in comparison with the magnetic susceptibility of Fermi system in differentsituations, the paper concludes as follows.1) At high temperature the magnetic susceptibilitydecreases with the temperature increasing whereas it increases with the temperatureincreasing at low temperature.2) The attraction effect on the magnetic susceptibility isstronger than that of repulsion effect both at high and low temperature; Thereby, theinteraction effect on the magnetic susceptibility can be ignored in strongly relativistic Fermisystems.3) The relativistic effects on the magnetic susceptibility must be taken intoconsideration only on condition of low temperature in weekly relativistic Fermi systems whilethe effects can be ignored on other conditions. What’s more, at high temperature, the magneticsusceptibility in strongly relativistic Fermi system is less than that in weakly relativistic Fermisystem whereas the opposite is true at low temperature.