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The Specific Heat of a Trapped Fermi Gas: an Analytical Approach

José M. B. Noronha, David J. Toms, Typeset Using Revtex

Published Jan 1, 2008• 6 citations
OpenAlex

Abstract

We find an analytical expression for the specific heat of a Fermi gas in a harmonic trap using a semi-classical approximation. Our approximation is valid for kBT � �wx,y,z and in this range it is shown to be highly accurate. We comment on the semi-classical approximation, presenting an explanation for this high accuracy.

Related papers

The specific heat of a trapped Fermi gas: An analytical approach

J. M B Noronha, David J. Toms

We find an analytical expression for the specific heat of a Fermi gas in a harmonic trap using a semi-classical approximation. Our approximation is valid for k(B)T ≥ hw(x, y, z) and in this range it is shown to be highly accurate. We comment on the semi-classical approximation, presenting an explanation for this high accuracy. (C) 2000 Elsevier Science B.V.

•Dec 31, 2000•0 citations

Maximum trap range and equation of state for Fermi gas in potential trap

Yuan Du-Qi

In the Thomas-Fermi semi-classical approximation, the maximal trap range and the real trap volume of ideal Fermi gas in an n-dimensional potential trap are gaven, and the relevant equations of state are derived. These results indicate that the maximal trap range and the real pressure of trapped gas are related to the potential field and the chemical potential of the free and ideal Fermi system. When the Thomas-Fermi approximate is valid and the condition ((kT)/(hω))2 ((16π2g)/(9N))2/3<<1 is satisfied, the application of the equation of state to three-dimensional spherical symmetry harmonic trap yields the result that the change of pressure is not obvious when the temperature changes, but the change of pressure is closely related to mass of particle, number of particles and the frequency of harmonic potential.

Acta Physica Sinica•Jan 1, 2011•2 citations

Analytic treatment of interacting Fermi gas in an arbitrary dimensional harmonic trap

Hiroyuki Yoshimoto, Susumu Kurihara

We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground-state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that the Thomas–Fermi approximation agrees well with the exact results for any dimension even though the system is small. In the high-temperature (classical) region, we find the interaction energy decreases in proportion to T − d /2 , where T is the temperature and d is the dimension of the system.

arXiv:cond-mat/0210198•Journal of Physics A Mathematical and General•Oct 8, 2003•6 citations

Fermi Gas in Harmonic Oscillator Potentials

X. X. Yi, J C Su

Assuming the validity of grand canonical statistics, we study the properties of a spin polarized Fermi gas in harmonic traps. Universal forms of Fermi temperature T F , internal energy U and the specific heat per particle of the trapped Fermi gas are calculated as a function of particle number, and the results are compared with those of infinite number particles.

arXiv:quant-ph/0003030•Physica Scripta•Aug 1, 1999•6 citations

Exact particle and energy densities for a noninteracting Fermi gas in a harmonic trap

Xian Zhi Wang

The exact particle and energy densities for a noninteracting Fermi gas at any temperature in a d -dimensional harmonic trap are obtained, and they are expressed by the gamma function and the Laguerre polynomials. The obtained analytical expressions are rapidly converging series and may be conveniently used for the numerical calculations. These expressions can be used for the comparison with the experimental results and for the test of the local density approximation.

Journal of Physics A Mathematical and General•Oct 28, 2002•5 citations

ON THE DERIVATION OF THERMODYNAMIC QUANTITIES OF IDEAL FERMI GAS IN HARMONIC TRAP

PHẠM NGUYỄN THÀNH VINH

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.

HUE UNIVERSITY JOURNAL OF SCIENCE NATURAL SCIENCE•Jul 15, 2017•0 citations
In the Thomas-Fermi semi-classical approximation, the maximal trap range and the real trap volume of ideal Fermi gas in an n-dimensional potential trap are gaven, and the relevant equations of state are derived. These results indicate that the maximal trap range and the real pressure of trapped gas are related to the potential field and the chemical potential of the free and ideal Fermi system. When the Thomas-Fermi approximate is valid and the condition ((kT)/(hω))2 ((16π2g)/(9N))2/3<<1 is satisfied, the application of the equation of state to three-dimensional spherical symmetry harmonic trap yields the result that the change of pressure is not obvious when the temperature changes, but the change of pressure is closely related to mass of particle, number of particles and the frequency of harmonic potential.
We study normal state properties of an interacting Fermi gas in an isotropic harmonic trap of arbitrary dimensions. We exactly calculate the first-order perturbation terms in the ground-state energy and chemical potential, and obtain simple analytic expressions of the total energy and chemical potential. At zero temperature, we find that the Thomas–Fermi approximation agrees well with the exact results for any dimension even though the system is small. In the high-temperature (classical) region, we find the interaction energy decreases in proportion to T − d /2 , where T is the temperature and d is the dimension of the system.
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.