Modelling Bose-condensed gases at finite temperatures with $N$-body simulations

TL;DR

This paper develops a numerical simulation framework for finite-temperature Bose-Einstein condensates, combining a generalized Gross-Pitaevskii equation with a kinetic model for thermal excitations, and applies it to study collective modes.

Contribution

It introduces a comprehensive 3D numerical scheme for simulating Bose-condensed gases at finite temperatures, integrating condensate and thermal cloud dynamics with Monte Carlo collision treatment.

Findings

Simulation of monopole mode in spherical trap shows frequency shifts and damping.

Numerical scheme confirms previous theoretical approximations.

Results validate the coupling effects between condensate and thermal cloud.

Abstract

We consider a model of a dilute Bose-Einstein condensed gas at finite temperatures, where the condensate coexists in a trap with a cloud of thermal excitations. Within the ZGN formalism, the dynamics of the condensate is described by a generalized Gross-Pitaevskii equation, while the thermal cloud is represented by a semiclassical kinetic equation. Our numerical approach simulates the kinetic equation using a cloud of representative test particles, while collisions are treated by means of a Monte Carlo sampling technique. A full 3D split-operator Fast Fourier Transform method is used to evolve the condensate wavefunction. We give details regarding the numerical methods used and discuss simulations carried out to test the accuracy of the numerics. We use this scheme to simulate the monopole mode in a spherical trap. The dynamical coupling between the condensate and thermal cloud is responsible for frequency shifts and damping of the condensate collective mode. We compare our results to previous theoretical approaches, not only to confirm the reliability of our numerical scheme, but also to check the validity of approximations which have been used in the past.