Scattering from Complex Potentials

F. Guillod, P. Huguenin

Rainer Dick

Peter Fröbrich, R. Lipperheide

Abstract In the preceding chapter we have discussed the semiclassical approximation to quantum scattering theory, where the dynamics is described in terms of classical trajectories. By analytic continuation of these trajectories into the complex plane the treatment has even been extended to the scattering by complex, i.e. absorptive, potentials.

Emilio d’Emilio, Luigi E. Picasso

Wang Tian-Yuan

We consider the one-dimensional nonlinear Schrödinger equations that describe the dynamics of a Bose–Einstein Condensates with time-dependent scattering length in a complex potential. Our results show that as long as the integrable relation is satisfied, exact solutions of the one-dimensional nonlinear Schrödinger equation can be found in a general closed form, and interactions between two solitons are modulated in a complex potential. We find that the changes of the scattering length and trapping potential can be effectively used to control the interaction between two bright soliton.

Florian A. Scheck