Multiple-scale analysis for resonance reflection by a one-dimensional rectangular barrier in the Gross-Pitaevskii problem

Journal Article · Thu Oct 15 04:00:00 EDT 2009 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.80.045601· OSTI ID:21316519

Ishkhanyan, H A; Krainov, V P ^[1]

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1. Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Moscow Region (Russian Federation)

We consider a quantum above-barrier reflection of a Bose-Einstein condensate by a one-dimensional rectangular potential barrier, or by a potential well, for nonlinear Schroedinger equation (Gross-Pitaevskii equation) with a small nonlinearity. The most interesting case is realized in resonances when the reflection coefficient is equal to zero for the linear Schroedinger equation. Then the reflection is determined only by small nonlinear term in the Gross-Pitaevskii equation. A simple analytic expression has been obtained for the reflection coefficient produced only by the nonlinearity. An analytical condition is found when common action of potential barrier and nonlinearity produces a zero reflection coefficient. The reflection coefficient is derived analytically in the vicinity of resonances which are shifted by nonlinearity.

• OSTI ID: 21316519
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 80; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOSE-EINSTEIN CONDENSATION
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
OPTICS
POTENTIALS
REFLECTION
RESONANCE
SCHROEDINGER EQUATION