The Study Of Thermodynamic Properties Of A Fermi System With The Generalized Uncertainty Principle

When considering the generalized uncertainty principle, microscopic state of state density must be revised. Under this amendment, In the high-energy, high temperature conditions, statistical physics calculations under the generalized uncertainty principle of the calculation results of statistical physics and traditional ideas have very big disparity! For example, the classical ideal gas, when temperature tends to infinity, the system of the non-zero level (excited) on the number of particles tend to a certain value, then if add the number of particles of the systems, they will be zero level (ground state)"condensed"(condensing temperature tends to infinity)! The system will no longer increases when to limit the temperature, appear the themaximum energy. In the non-commutative space, the heat capacity with temperature tends to infinity and close to0! Traditional statistical physics ideal gas does not appear in the classic "high temperature condensation","energy limit." At the same time the heat capacity in the usual high temperature circumstances are the result of the equipartition theorem, has nothing to do with temperature, is a constant.Under the condition of low temperature, considering the generalized uncertainty principle of statistical physics, though not like the extremely high temperature scene of subversive of the traditional concept of change, but there are still some minor correction. Meanwhile Fermi gas at low temperatures under certain restrictions BCS condensation can occur, at the same time, through electronic and phonon interactions contribute to mutual transformation between the BEC and BCS. The generalized uncertainty principle under the low temperature thermodynamic properties of the Fermi gas has certain theoretical value and practical value. In this paper, study the Fermi system on the basis of considering the generalized uncertainty principle, and study the properties of the Fermi system under the condition of at low temperature. Do the following concrete work.First, when considering the generalized uncertainty principle, microscopic state of state density must be revised. Under this amendment, study the thermodynamic properties at low temperatures of the ideal Fermi gas. Calculate the system’s internal energy and heat capacity and so on various major thermodynamic functions. While, the specific simulation calculation of copper electron gas is given as an example.In which, the results of the generalized uncertainty principle which is not consider has carried on the comparative analysis. The effects of the generalized uncertainty principle on the properties of the systems are discussed.Secondly, on the basis of the modified state density using semi-classical (Thomas-Fermi) approximation method, the properties of ideal Fermi gas are studied under the limited research in the gravitational field of generalized uncertainty principle. The internal energy and the constant volume heat capacity in which the analytical expressions under the condition of low temperature are given. While, the specific simulation calculation of copper electron gas is given as an example.In which, the results of the generalized uncertainty principle which is not consider has carried on the comparative analysis. Study found that when considering the generalized uncertainty principle, fermion should not only follow the restrictions of the Pauli exclusion principle also increase should follow the’the minimum length’limit, this limit has the effects on the ideal Fermi system properties in the gravitational field.Finally the generalized uncertainty principle of’the minimum length’limit on the basis of constraint pseudo-potential method is used to study under the weakly interacting Fermi gas, the nature of GUP always improved the interaction, when a>0, the system’s chemical potential,Internal energy and heat capacity than the pure constraint method and the traditional ideal gas is increased. When a<0, the system’s chemical potential,internal energy and heat capacity than the pure constraint method and the traditional ideal gas is reduced; Without external potential, the interaction between particles does not affect the constant volume heat capacity, but as a result of the generalized uncertainty principle of low-energy state after filling particles to upper state transition, as a result, the heat capacity increases, when the system before the thermodynamic quantities are returned to the correct conclusion.