Destruction of the beating effect for a nonlinear Schrödinger equation

DOI10.1007/s002200200643zbMath1001.81011OpenAlexW2044078089MaRDI QIDQ1849543

Vincenzo Grecchi, Andrea Sacchetti, André Martinez

Publication date: 1 December 2002

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s002200200643

zbMATH Keywords

nonlinear perturbationtwo-level systemsymmetric double-well potentialcritical value of the perturbation parameterfirst bifurcation of the fundamental statemolecular localization

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of operator theory in the physical sciences (47N50) NLS equations (nonlinear Schrödinger equations) (35Q55) Perturbation theories for operators and differential equations in quantum theory (81Q15) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Molecular physics (81V55)

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Exponential times in the one-dimensional Gross-Pitaevskii equation with multiple well potential ⋮ The quantum beating and its numerical simulation ⋮ Nonlinear Schrödinger equations with multiple-well potential ⋮ Bifurcation and stability for nonlinear Schrödinger equations with double well potential in the semiclassical limit ⋮ The Landau-Zener Transition and the Surface Hopping Method for the 2D Dirac Equation for Graphene ⋮ Interaction of coherent states for Hartree equations ⋮ Stationary states for nonlinear Schrödinger equations with periodic potentials ⋮ Nonlinear double well Schrödinger equations in the semiclassical limit ⋮ On a mathematical model for a damped and driven double-well Bose-Einstein condensate

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