  We discuss the non-equilibrium time evolution of the phase field in the
sine-Gordon model using two very different approaches: the truncated Wigner
approximation and the truncated conformal space approach. We demonstrate that
the two approaches agree for a period covering the first few oscillations,
thereby giving a solid theoretical prediction in the framework of sine-Gordon
model, which is thought to describe the dynamics of two bosonic condensates in
quasi-one-dimensional traps coupled via a Josephson tunneling term. We
conclude, however, that the recently observed phase-locking behavior cannot be
explained in terms of homogeneous sine-Gordon dynamics, which hints at the role
of other degrees of freedom or inhomogeneity in the experimental system.
