Fizika Nizkikh Temperatur: Volume 44, Number 7 (July 2018), p. 865-876    ( to contents , go back )

Compact discrete breathers on flat-band networks

C. Danieli1, A. Maluckov1,2, and S. Flach1,3

1Center for Theoretical Physics of Complex Systems, Institute for Basic Science, Daejeon, Korea

2Vinca Institute for Nuclear Sciences, University of Belgrade, Serbia

3New Zealand Institute for Advanced Study, Massey University, Auckland, New Zealand
E-mail: sergejflach@googlemail.com

Received March 1, 2018

Abstract

Linear wave equations on flat-band networks host compact localized eigenstates (CLS). Nonlinear wave equations on translationally invariant flat-band networks can host compact discrete breathers-time-periodic and spatially compact localized solutions. Such solutions can appear as one-parameter families of continued linear compact eigenstates, or as discrete sets on families of non-compact discrete breathers, or even on purely dispersive networks with fine-tuned nonlinear dispersion. In all cases, their existence relies on destructive interference. We use CLS amplitude distribution properties and orthogonality conditions to derive existence criteria and stability properties for compact discrete breathers as continued CLS.

PACS: 71.10.–w Theories and models of many-electron systems;
PACS: 71.10.Fd Lattice fermion models (Hubbard model, etc.).

Key words: compact localized eigenstates, discrete breathers, flat band.

Published online: May 28, 2018

Download 690948 byte View Contents