Effective mass theorems for nonlinear Schroedinger equations

2004/10/05 by Christof Sparber, Sparber, Christof · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #35B25 #35B27 #35Q55 #74Q10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Numerical methods for differential equations #math-ph #math.AP #math.MP #msc:35B25 #msc:35B27 #msc:35Q55 #msc:74Q10

paper · pdf · doi:10.48550/arxiv.math-ph/0410017

22 pages; slightly shortened version, some typos corrected, some explanations added

openalex publication_date 2004/10/05 · arxiv created 2005/02/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider time-dependent nonlinear Schroedinger equations subject to smooth, lattice-periodic potentials plus additional confining potentials, slowly varying on the lattice scale. After an appropriate scaling we study the homogenization limit for vanishing lattice spacing. Assuming well prepared initial data, the resulting effective dynamics is governed by a homogenized nonlinear Schroedinger equation with an effective mass tensor depending on the initially chosen Bloch eigenvalue. The given results rigorously justify the use of the effective mass formalism for the description of Bose-Einstein condensates on optical lattices.

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