Nonlinear Stark-Wannier equation

2017/03/21 by Andrea Sacchetti, Sacchetti, Andrea
Computer Science · Mathematics · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Quantum chaos and dynamical systems #math-ph #math.MP #msc:35Q55 #msc:81Qxx #msc:81T25

paper · pdf · doi:10.48550/arxiv.1703.07245

27 pages, 2 Figures

arxiv created 2018/11/30 · arxiv updated 2018/12/03

Abstract

In this paper we consider stationary solutions to the nonlinear one-dimensional Schroedinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark-Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs when the ratio between the effective nonlinearity strength and the tilt of the external field increases.

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