Derivation of the tight-binding approximation for time-dependent nonlinear Schr\"odinger equations
Mathematical Physics
2019-10-10 v2 math.MP
Quantum Physics
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.
Cite
@article{arxiv.1902.09143,
title = {Derivation of the tight-binding approximation for time-dependent nonlinear Schr\"odinger equations},
author = {Andrea Sacchetti},
journal= {arXiv preprint arXiv:1902.09143},
year = {2019}
}
Comments
Revised version - 20 pages