Time-dependent linear response of an inhomogeneous Bose superfluid: Microscopic theory and connection to current-density functional theory

TL;DR

This paper develops a microscopic, current-density functional framework for analyzing the linear response of inhomogeneous Bose superfluids, connecting microscopic equations to hydrodynamic and Landau theories.

Contribution

It introduces a detailed microscopic formalism for superfluid response functions and extends it to include current density coupling, linking microscopic theory with hydrodynamic models.

Findings

Derived a microscopic formula for superfluid density.

Established local-density expressions for first and second sound velocities.

Connected microscopic response functions to hydrodynamic and Landau theories.

Abstract

The dynamics of a confined fluid of Bose atoms is treated within the linear response regime, with a view to establishing a current-density functional formalism for an inhomogeneous superfluid state. After evaluating in full detail a simplified case of an external coupling to the density and phase of the condensate, the theory is extended to include the coupling to the total current density. The Kohn-Sham response functions of the condensate and all the exchange-correlation kernels for the superfluid are introduced from the microscopic equations of motion and are expressed in a physically transparent way through functional derivatives of correlation functions. A microscopic formula for the superfluid density is derived and used to introduce a generalized hydrodynamic approach for a weakly inhomogeneous two-fluid model in isothermal conditions. Local-density expressions are thereby derived for the velocities of first and second sound in the weakly inhomogeneous superfluid and for visco-elastic functions describing the transition from the hydrodynamic to the collisionless regime. Landau's hydrodynamic theory and known results in Green's functions language are recovered in the limiting case of a homogeneous superfluid.