The Unitary Fermi Gas: From Monte Carlo to Density Functionals

Abstract

In this chapter, we describe three related studies of the universal physics of two-component unitary Fermi gases with resonant short-ranged interactions. First we discuss an ab initio auxiliary field quantum Monte Carlo technique for calculating thermodynamic properties of the unitary gas from first principles. We then describe in detail a Density Functional Theory (DFT) fit to these thermodynamic properties: the Superfluid Local Density Approximation (SLDA) and its Asymmetric (ASLDA) generalization. We present several applications, including vortex structure, trapped systems, and a supersolid Larkin-Ovchinnikov (FFLO/LOFF) state. Finally, we discuss the time-dependent extension to the density functional (TDDFT) which can describe quantum dynamics in these systems, including non-adiabatic evolution, superfluid to normal transitions and other modes not accessible in traditional frameworks such as a Landau-Ginzburg, Gross-Pitaevskii, or quantum hydrodynamics.

Nuclear density functional theory with a semi-contact 3-body interaction

“…This very simple form has been used in Refs. [11,12] (see also [13]) to suggest a rather minimalist DFT-LDA functional for unitary gas where the energy density writes…”

Computational nuclear quantum many-body problem: The UNEDF project

“…In order to avoid the nonlocal character of the DFT extension to superfluid systems, the superfluid local density approximation (SLDA) and its time-dependent extension TDSLDA have been developed [145,146,147,148,149,150,151,152,153,154].…”

“…The nuclear EDFs should satisfy the usual symmetries [68] and the consistency with the best available ab initio results. The numerical implementation of the SLDA and TD-SLDA equations leads to hundreds of thousands of coupled nonlinear 3D time-dependent PDEs, which are solved by using the discrete variable representation approach [155,156] on desktops [147,148,149,150] and-as a result of UNEDF collaborations with computer scientistsleadership-class supercomputers [150,151,152,153,154]. In Fig.…”

Critical velocity, vortex shedding, and drag in a unitary Fermi superfluid

“…Note that although in a superfluid there is no frictional viscosity, nonetheless shear stress may arise from density (pressure) gradients (third term in Eq. (10). As a consequence, vortex formation and drag are possible even with no viscosity.…”

“…Recently it has been remarked [10] that the superfluid unitary Fermi gas can be efficiently described at zero temperature by phenomenological density functional theory. Density functionals of different flavours have been proposed by different theoretical groups.…”