We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size ${l}_{\ensuremath{\perp}}$. In the dilute limit ($n{l}_{\ensuremath{\perp}}\ensuremath{\ll}1$, where $n$ is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length ${a}_{F}$ . When ${l}_{\ensuremath{\perp}}/{a}_{F}$ goes from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at ${a}_{F}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}n{l}_{\ensuremath{\perp}}^{2}$. In conclusion, we discuss experimental implications of these results.We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size ${l}_{\ensuremath{\perp}}$. In the dilute limit ($n{l}_{\ensuremath{\perp}}\ensuremath{\ll}1$, where $n$ is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length ${a}_{F}$. When ${l}_{\ensuremath{\perp}}/{a}_{F}$ goes from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at ${a}_{F}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}n{l}_{\ensuremath{\perp}}^{2}$. In conclusion, we discuss experimental implications of these results.

arXiv:cond-mat/0402276Physical Review LettersAug 25, 2004104 citations

The one-dimensional Fermi gas model

Jenő Sólyom

Annals of the Israel Physical SocietyJan 1, 19780 citations

THERMODYNAMICS OF THE FERMI GAS IN A NANOTUBE

Yu. M. Poluéktov, A. A. Soroka

For the ideal Fermi gas that fills the space inside a cylindrical tube, there are calculated the thermodynamic characteristics in general form for arbitrary temperatures, namely: the thermodynamic potential, energy, entropy, equations of state, heat capacities and compressibilities. All these quantities are expressed through the introduced standard functions and their derivatives. The radius of the tube is considered as an additional thermodynamic variable. It is shown that at low temperatures in the quasi-one-dimensional case the temperature dependencies of the entropy and heat capacities remain linear. The dependencies of the entropy and heat capacities on the chemical potential have sharp maximums at the points where the filling of a new discrete level begins. The character of dependencies of thermodynamic quantities on the tube radius proves to be qualitatively different in the cases of fixed linear and fixed total density. At the fixed linear density these dependencies are monotonous and at the fixed total density they have an oscillating character. Key words: Fermi particle, nanotube, thermodynamic functions, low-dimensional systems, equation of state, heat capacity, compressibilityFor the ideal Fermi gas that fills the space inside a cylindrical tube, there are calculated the thermodynamic characteristics in general form for arbitrary temperatures, namely: the thermodynamic potential, energy, entropy, equations of state, heat capacities and compressibilities. All these quantities are expressed through the introduced standard functions and their derivatives. The radius of the tube is considered as an additional thermodynamic variable. It is shown that at low temperatures in the quasi-one-dimensional case the temperature dependencies of the entropy and heat capacities remain linear. The dependencies of the entropy and heat capacities on the chemical potential have sharp maximums at the points where the filling of a new discrete level begins. The character of dependencies of thermodynamic quantities on the tube radius proves to be qualitatively different in the cases of fixed linear and fixed total density. At the fixed linear density these dependencies are monotonous and at the fixed total density they have an oscillating character. Key words: Fermi particle, nanotube, thermodynamic functions, low-dimensional systems, equation of state, heat capacity, compressibility

arXiv:1704.03317East European Journal of PhysicsJan 1, 20171 citation

Ground-state energy of a dilute fermi gas

R. F. Bishop

Annals of PhysicsMay 1, 197364 citations

n

is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length

{a}_{F}

. When ${l}_{\ensuremath{\perp}}/{a}_{F}$ goes from $\ensuremath{-}\ensuremath{\infty}$ to $+\ensuremath{\infty}$, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at ${a}_{F}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}n{l}_{\ensuremath{\perp}}^{2}$. In conclusion, we discuss experimental implications of these results.