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arXiv:1009.3953

Low temperature thermodynamic properties of a polarized Fermi gas in a quartic trap

Mark J. DelloStritto, Theja N. De Silva

Published Sep 20, 2010• 0 citations
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Abstract

We study low temperature thermodynamic properties of a polarized Fermi gas trapped in a quartic anharmonic potential. We use a semi classical approximation and a low temperature series expansion method to derive analytical expressions for various thermodynamic quantities. These quantities include the total energy, particle number, and heat capacity for both positive and negative anharmonic confinements.

DOI
10.48550/arxiv.1009.3953

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We study low temperature thermodynamic properties of a polarized Fermi gas trapped in a quartic anharmonic potential. We use a semi classical approximation and a low temperature series expansion method to derive analytical expressions for various thermodynamic quantities. These quantities include the total energy, particle number, and heat capacity for both positive and negative anharmonic confinements.
In this paper I derive the static and dynamic properties of two differnt fermionic cold gas system. I derive the thermodynamic properties of a fully polarized noninteracting fermi gas in a quartic trap using a semiclassical approach and a low temperature series expansion method. I also introduce the recently discovered quantity Contact and derive several universal relations associated with it. In order to derive the contact, I use two different methods: a ground-state energy fucntional based on asymptotic limits and Monte Carlo calculations, and BCS Mean Field Theory. I use the universal relations associated with Contact to derive several static and dynamic properties of a balanced strongly interacting gas of fermions with two spin states and large scattering length. The static properties include the total energy, contact density, and polytropic index of the system, and the dynamic properties include the collective oscillations of the trap, the structure factor, and an alternate derivation of the polytropic index. The collective oscillation frequencies are found using both hydrodynamic theory and a sum rule approach and are presented in terms of the contact and homogenous energy. It is found that the static and dynamic properties derived for this system agree well with experimental data and alternative theoretical approaches.
Based on the semiclassical(Thomas-Fermi) approximation,the macrocanonical partition function and macrocanonical potential of a relativistic Fermi gas in a general external potential in any dimensional space are studied.The general analytical expressions of the total particle number N,total energy U and heat capacity C have been derived with thermodynamic fundamental equations,where N,U and C are expressed by the modified Bessel function.Moreover,the analytical expressions of the total energy,chemical potential and heat capacity in the high-and low-temperature approximations are given.From these results,how the characteristics of the Fermi gas depend on various factors is discussed.
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In this paper, we provide comprehensive study of the thermodynamic quantities of the ideal Fermi gas confined in a three-dimensional harmonic trap by using the properties of Fermi – Dirac integral function both analytically and numerically. The dependences of the chemical potential, total energy and heat capacity on the temperature are obtained via the appropriately approximated analytic formulae. Afterwards, the results are compared with the exact numerical ones in order to evaluate the applicability of these formulae.