Details

Autor(en) / Beteiligte

• Hari, Lysianne

Titel

PROPAGATION OF SEMICLASSICAL WAVE PACKETS THROUGH AVOIDED EIGENVALUE CROSSINGS IN NONLINEAR SCHRÖDINGER EQUATIONS

Ist Teil von

• Journal of the Institute of Mathematics of Jussieu, 2016-04, Vol.15 (2), p.319-365

Ort / Verlag

Cambridge, UK: Cambridge University Press

Erscheinungsjahr

2016

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We study the propagation of wave packets for a one-dimensional system of two coupled Schrödinger equations with a cubic nonlinearity, in the semiclassical limit. Couplings are induced by the nonlinearity and by the potential, whose eigenvalues present an avoided crossing: at one given point, the gap between them reduces as the semiclassical parameter becomes smaller. For data which are coherent states polarized along an eigenvector of the potential, we prove that when the wave function propagates through the avoided crossing point there are transitions between the eigenspaces at leading order. We analyze the nonlinear effects, which are noticeable away from the crossing point, but see that in a small time interval around this point the nonlinearity’s role is negligible at leading order, and the transition probabilities can be computed with the linear Landau–Zener formula.