Thermodynamics of Low-Dimensional Trapped Fermi Gases

Abstract

The effects of low dimensionality on the thermodynamics of a Fermi gas trapped by isotropic power-law potentials are analyzed. Particular attention is given to different characteristic temperatures that emerge, at low dimensionality, in the thermodynamic functions of state and in the thermodynamic susceptibilities (isothermal compressibility and specific heat). An energy-entropy argument that physically favors the relevance of one of these characteristic temperatures, namely, the nonvanishing temperature at which the chemical potential reaches the Fermi energy value, is presented. Such an argument allows interpreting the nonmonotonic dependence of the chemical potential on temperature, as an indicator of the appearance of a thermodynamic regime, where the equilibrium states of a trapped Fermi gas are characterized by larger fluctuations in energy and particle density as is revealed in the corresponding thermodynamics susceptibilities.

Finite-temperature dynamics of shock waves in an ultracold Fermi gas

“…The chemical potential of the original 1D Fermi gas confined in a box at zero temperature is given by μ = E N − E 0 = ω N − ω 0 , and hence where N is the number of Fermi particles. For finite temperatures T , the chemical potential is [54]…”