Dynamical Hartree-Fock-Bogoliubov Theory of Vortices in Bose-Einstein Condensates at Finite Temperature

TL;DR

This paper introduces a novel method combining the continuity equation with an orthogonalized Hartree-Fock-Bogoliubov formalism to predict vortex dynamics in finite-temperature Bose-Einstein condensates, validated through simulations.

Contribution

It develops a self-consistent approach to determine vortex precession frequencies and stationary states in rotating BECs at finite temperature, incorporating vortex arrays.

Findings

Accurately predicts vortex precession frequencies.

Provides stationary solutions for rotating BEC systems.

Validates predictions with time-dependent simulations.

Abstract

We present a method utilizing the continuity equation for the condensate density to make predictions of the precessional frequency of single off-axis vortices and of vortex arrays in Bose-Einstein condensates at finite temperature. We also present an orthogonalized Hartree-Fock-Bogoliubov (HFB) formalism. We solve the continuity equation for the condensate density self-consistently with the orthogonalized HFB equations, and find stationary solutions in the frame rotating at this frequency. As an example of the utility of this formalism we obtain time-independent solutions for quasi-two-dimensional rotating systems in the co-rotating frame. We compare these results with time-dependent predictions where we simulate stirring of the condensate.