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In this work we consider the non-equilibrium dynamics of two tunnel coupledbosonic gases which are created from the coherent splitting of aone-dimensional gas. The consequences of the tunneling both in thenon-stationary regime as well as at large time are investigated and comparedwith equilibrium results. In particular, within a semiclassical approximation,we compute correlation functions for the relative phase which areexperimentally measurable and we observe a transient regime displayingoscillations as a function of the distance. The steady regime is very wellapproximated by a thermal state with a temperature independent of the tunnelingstrength.

Relaxation dynamics of two coherently coupled one-dimensional bosonic gases