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arXiv · 1902.09143

Derivation of the tight-binding approximation for time-dependent nonlinear Schr\"odinger equations

Andrea Sacchetti
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Abstract

In this paper we consider the nonlinear one-dimensional time-dependent Schroedinger equation with a periodic potential and a local perturbation. In the limit of large periodic potential the time behavior of the wavefunction can be approximated, with a precise estimate of the remainder term, by means of the solution to the discrete nonlinear Schroedinger equation of the tight-binding model.

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Andrea Sacchetti. 2019-02-25. Derivation of the tight-binding approximation for time-dependent nonlinear Schr\"odinger equations. https://arxiv.org/abs/1902.09143

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