Regensburg 2016 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 26: Poster - Quanten Systems
DY 26.9: Poster
Dienstag, 8. März 2016, 18:15–21:00, Poster C
Stationary waves on nonlinear quantum graphs — Sven Gnutzmann1 and •Daniel Waltner2 — 1School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK — 2Fakultät für Physik, Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany
We present a general framework for solving the stationary nonlinear Schrödinger equation (NLSE) on a network of one-dimensional wires modelled by a metric graph with suitable matching conditions at the vertices. For the cubic NLSE the solutions are given by Jacobi elliptic functions. For sufficiently small amplitudes we use canonical perturbation theory that allows to extract the leading nonlinear corrections over large distances. Simple closed and scattering graphs serve as examples.