Universal relations for Fermi gases in arbitrary dimension

Tara E. Drake, John Gaebler, Jayson Stewart +1 more

Manuel Valiente, Nikolaj Thomas Zinner, Klaus Mølmer

We consider spin-$1/2$ Fermi gases in arbitrary, integer, or noninteger spatial dimensions, interacting via a Dirac $\ensuremath{\delta}$ potential. We first generalize the method of Tan's distributions and implement short-range boundary conditions to arbitrary dimension and we obtain a set of universal relations for the Fermi gas. Three-dimensional scattering under very general conditions of transversal confinement is described by an effectively reduced-dimensional scattering length, which we show depends on the three-dimensional scattering length in a universal way. Our formula for noninteger dimensions interpolates between the known results in integer dimensions 1, 2, and 3. Without any need to solve the associated multichannel scattering problem, we find that confinement-induced resonances occur in all dimensions different from $D=2$, while reduced-dimensional contacts, related to the tails of the momentum distributions, are connected to the three-dimensional contact by a correction factor of purely geometric origin.

Sami M. Al-Jaber

Zhan Li-bo

we derive the quantum state density, the relation of internal energy and the pressure of arbitrary dimensional ideal gases that have energy spectrum of e = ap5 , and then offer the universal descriptions of chemistry potential, internal energy ,degenerate pressure and relative fluctuation of arbitrary dimensional ideal Fermi gases, through analysis and comparison, we draw a conclusion that when temperature approaches zero, thermodynamic quantities of high degenerate Fermi gases under low temperature trend to that of the complete degenerate Fermi gases.

Michael Köhl

W. Zwerger

The experimental realization of stable, ultracold Fermi gases near a Feshbach resonance allows to study gases with attractive interactions of essentially arbitrary strength. They extend the classic paradigm of BCS into a regime which has never been accessible before. We review the theoretical concepts which have been developed in this context, including the Tan relations and the notion of fixed points at zero density, which are at the origin of universality. We discuss in detail the universal thermodynamics of the unitary Fermi gas which allows a fit free comparison between theory and experiment for this strongly interacting system. In addition, we adress the consequences of scale invariance at infinite scattering length and the subtle violation of scale invariance in two dimensions. Finally we discuss the Fermionic excitation spectrum accessible in momentum resolved RF-spectroscopy and the origin of universal lower bounds for the shear viscosity and the spin diffusion constant.