Thermodynamic Properties Of Fermi Gas In A General External Potential Under Generalized Uncertainty Principle

When considering generalized uncertainty principle,the quantum state density in statistical physics must be revised.When considering the amendment in high energy and high temperature conditions,some calculation results in statistical physics are very different from the traditional results.For example,the classical ideal gas,when the temperature increased to infinity,particle numbers of excited state in the system will approach a fixed value.At this moment,if the particle numbers continues to increase,they will be "condensed"at ground state.When comes to extreme temperature,the energy of the system does not increase,appear the maximum energy.In traditional statistical physics,the classical ideal gas doesn’t have an "energy cap",the heat capacity of the system is constant,independent of temperature.Take into account the generalized uncertainty principle,under the condition of low temperature in statistical physics though it is not similar to very high temperature conditions are the result of the traditional difference,but there are still some minor correction.In addition,the Fermi gas of low temperature under certain constraints can also occur condense,study the thermodynamic properties of the Fermi gas under the generalized uncertainty principle has a certain theoretical and practical value.In this paper,we study the properties of Fermi system in generalized external potential by the modification of generalized uncertainty principle.This is the following:In Chapter 1,the Generalized Uncertainty Principle,Uncertainty Principle and the research status and significance of Fermi gas are briefly introduced.In Chapter 2,on the basis of considering the effects of generalized uncertainty principle and using quantum statistical method deduce the grand partition function of the Fermi system in general external potential,which is deduced the mean number,internal energy and heat capacity,and studied the Fermi energy of Fermi gas in different external potential.In Chapter 3,thermodynamic properties of Fermi system in harmonic potential are studied under generalized uncertainty principle.By numerical simulation,the change of chemical potential,internal energy and heat capacity be obtained.The thermodynamic properties of weakly interacting Fermi systems in harmonic potential are also studied under generalized uncertainty principle,then influence of external potential,average particle density and generalized uncertainty principle on the thermodynamic properties of Fermi gas is analyzed.Chapter 4,the thermodynamic properties of the Fermi system in the finite potential are studied.The changes of chemical potential,internal energy and heat capacity of Fermi system in one-dimensional finite potential and two-dimensional finite potential are obtained by numerical simulation and analyzes the trend of their changes,and compares with the results of the three dimensional harmonic potential.