Energy decay for a system of Schr{ö}dinger equations in a wave guide
We prove exponential decay for a system of two Schr{ö}dinger equations in a wave guide, with coupling and damping at the boundary. This relies on the spectral analysis of the corresponding coupled Schr{ö}dinger 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.
math.AP↗