Implementing Galilean Invariance in Density Functional Calculations of a Unitary Fermi Gas

Adam Richie-Halford, University of Washington

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We discuss the time-dependent superfluid local density approximation (TDSLDA), an extension of the Hohenberg-Kohn density functional theory (DFT), applied to superfluid fermionic systems. Within the time-dependent density functional theory approach to the unitary Fermi gas one can use a range of energy density functionals with varying degrees of detail and accuracy. The most accurate energy density functional requires the introduction of an effective mass, which is different from the bare mass of the fermions. In order not to violate the Galilean invariance, one has to introduce additional terms, which depend on the current densities. In the ground state these additional terms play no role as currents are absent, but they become important when discussing excited states of the system and when currents can attain large values. The Galilean invariance is enforced locally, since for big systems separate parts of the system (which might or might not be in direct contact) might be moving at different velocities.

Abstract Author(s): Adam Richie-Halford, Aurel Bulgac, Kenneth J. Roche