Manuscrito
Almost Exponential Decay For A Coupled System Of Schrodinger Equations
Autor
Astaburuaga, M Angélica
Fernández-Jaña, Claudio Alonso
Charao, Ruy Coimbra
Perla-Menzala, Gustavo
Institución
Resumen
Let h =
(h1
h2
)
be a resonant solution of a linearly
coupled system of perturbed Schr odinger equations on the half
line[0;1), with Dirichlet boundary conditions at the origin. The
function h is then a generalized eigenvector of the related Hamil-
tonian system H that satis es an outgoing condition at in nity.
Then Hh = k2h, where the resonance k2 is complex with Im k2
negative. The main goal of this work is to show that the pres-
ence of resonance is manifested by an approximate exponential
behaviour. Indeed since the outgoing condition rules out square
integrability, we truncate h to an interval containing the support
of the perturbation and show that when the resonance is near the
real axis, the probability amplitude ⟨h; e�����iHth⟩ has a certain ex-
ponential behaviour in time. 18