Effective mass theorems for nonlinear Schroedinger equations

Details Effective mass theorems for nonlinear Schroedinger equations Effective mass theorems for nonlinear Schroedinger equations

2004-10-05

arxiv.org/abs/math-ph/0410017v2

Physics

Mathematical Physics

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

Scientific paper

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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