Energy decay for a system of Schr\"odinger equations in a wave guide
Abstract
We prove exponential decay for a system of two Schr\"odinger equations in a wave guide, with coupling and damping at the boundary. This relies on the spectral analysis of the corresponding coupled Schr\"odinger operator on the one-dimensional cross section. We show in particular that we have a spectral gap and that the corresponding generalized eigenfunctions form a Riesz basis.
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