Relative phase fluctuations of two coupled one-dimensional condensates

We study the relative phase fluctuations of two one-dimensional condensates coupled along their whole extension with a local single-atom interaction. The thermal equilibrium is defined by the competition between independent longitudinal thermally excited phase fluctuations and the coupling between the condensates which locally favors identical phase. We compute the relative phase fluctuations and their correlation length as a function of the temperature and the strength of the coupling.