Ideal Fermi Systems

Raj K. Pathria, Paul D. Beale

Tara E. Drake, Yoav Sagi, Rabin Paudel +3 more

The ideal (i.e., noninteracting), homogeneous Fermi gas, with its characteristic sharp Fermi surface in the momentum distribution, is a fundamental concept relevant to the behavior of many systems. With trapped Fermi gases of ultracold atoms, one can realize and probe a nearly ideal Fermi gas; however, these systems have a nonuniform density due to the confining potential. We show that the effect of the density variation, which typically washes out any semblance of a Fermi surface step in the momentum distribution, can be mitigated by selectively probing atoms near the center of a trapped gas. With this approach, we have directly measured a Fermi surface in momentum space for a nearly ideal gas, where the average density and temperature of the probed portion of the gas can be determined from the location and sharpness of the Fermi surface.

Zhao Sheng-pin

The study is on the thermodynamic properties of finite gravitational field weak degenerate ideal Fermi gas.Base on the Thomas-Fermi semiclassical approximation,after deriving the density of states of an ideal Fermi gas in finite gravitational field,the analytic formula of the chemical potential,internal energy and pressure under the condition of weak degeneration is obtained in this paper.The specific impact of the gravity field on the thermodynamic properties of weakly degenerate ideal Fermi gas is analyzed.The result showed that finite gravitational field has effect on the thermodynamic property of the system.

Raj K. Pathria

Vladimir S. Filinov

Over the last ten years the `fixed-node approximation', well known in the literature, has been widely used for a numerical treatment of thermodynamic properties of strongly correlated Fermi systems. Results of the direct path integral Monte Carlo simulation performed here show that the `fixed-node approximation' describes the thermodynamic properties of the strongly coupling fermions rather well at `weak and moderate' degeneracy. To analyse the reasons for the increasing difference between the `fixed-node approximation' and the results of direct path integral Monte Carlo simulations for highly degenerate fermions, the correctness of the `fixed-node approximation' for ideal Fermi systems has been analysed by analytical methods. A rigorous proof has been given of the fact that the exact Fermi function with index 3 / 2 describing the logarithm of the grand partition function of ideal fermions cannot be reproduced in the `fixed-node approximation', which means that the `fixed-node approximation' does not give the correct ideal Fermi gas limit.

Raj K. Pathria