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We prove exponential decay for a system of two Schr{\"o}dinger equations in awave guide, with coupling and damping at the boundary. This relies on thespectral analysis of the corresponding coupled Schr{\"o}dinger operator on theone-dimensional cross section. We show in particular that we have a spectralgap and that the corresponding generalized eigenfunctions form a Riesz basis.

Energy decay for a system of Schr{\"o}dinger equations in a wave guide