# Multiple-scale analysis for resonance reflection by a one-dimensional rectangular barrier in the Gross-Pitaevskii problem - Condensed Matter > Quantum Gases

Multiple-scale analysis for resonance reflection by a one-dimensional rectangular barrier in the Gross-Pitaevskii problem - Condensed Matter > Quantum Gases - Download this document for free, or read online. Document in PDF available to download.

Abstract: We consider a quantum above-barrier reflection of a Bose-Einstein condensateby a one-dimensional rectangular potential barrier, or by a potential well, fornonlinear Schroedinger equation Gross-Pitaevskii equation with a smallnonlinearity. The most interesting case is realized in resonances when thereflection coefficient is equal to zero for the linear Schroedinger equation.Then the reflection is determined only by small nonlinear term in theGross-Pitaevskii equation. A simple analytic expression has been obtained forthe reflection coefficient produced only by the nonlinearity. An analyticalcondition is found when common action of potential barrier and nonlinearityproduces a zero reflection coefficient. The reflection coefficient is derivedanalytically in the vicinity of resonances which are shifted by nonlinearity.

Author: ** H. A. Ishkhanyan, V. P. Krainov**

Source: https://arxiv.org/