Nonlinear time-dependent one-dimensional Schroedinger equation with double well potential

2002/12/05 by Andrea Sacchetti, Sacchetti, Andrea
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Opinion Dynamics and Social Influence #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0212024

arxiv created 2002/12/05 · openalex publication_date 2002/12/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest eigenvalues then, in the semiclassical limit, we show that the reduction of the time-dependent equation to a 2-mode equation gives the dominant term of the solution with a precise estimate of the error. By means of this stability result we are able to prove the destruction of the beating motion for large enough nonlinearity.

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