Classical field techniques for condensates in one-dimensional rings at finite temperatures

For a condensate in a one-dimensional ring geometry, we compare the thermodynamic properties of three conceptually different classical field techniques: stochastic dynamics, microcanonical molecular dynamics, and the classical field method. Starting from nonequilibrium initial conditions, all three methods approach steady states whose distribution and correlation functions are in excellent agreement with an exact evaluation of the partition function in the high-temperature limit. Our study helps to establish these various classical field techniques as powerful nonperturbative tools for systems at finite temperatures.