Discrete Breathers and Delocalization in Nonlinear Disordered Systems

Abstract

We find exact localized time-periodic solutions with frequencies inside the linearized spectrum [intraband discrete breathers (IDBs)] in random nonlinear models using a new self-consistent method. The IDB frequencies belong to intervals between forbidden gaps generated by resonances with the linear modes, becoming fat Cantor sets in infinite systems. When localized IDBs are continued versus frequency, they delocalize and become multisite IDBs (not predicted by existing theorems), which can propagate energy. Some implications for energy relaxation in glasses are discussed.

The Discrete Nonlinear Schrödinger Equation — 20 Years On

“…The transition between Anderson localized modes and breather states has more recently been extensively analysed in a series of papers by Kopidakis and Aubry for general coupled oscillator chains 69,71,70 (see also Archilla et al 10 for a slightly different model), and has to its larger parts been understood. The generic scenario, valid also for the DNLS model, is consistent with Feddersen's observations but too complicated to describe in detail here.…”

On the Problem of Dynamical Localization in the Nonlinear Schrödinger Equation with a Random Potential

“…The work of [31], presents results of extensive numerical calculation and heuristic arguments that shed light on this problem. It was also argued that nonlinearity may enhance discrete breathers [29]. In conclusion, it is not clear what is the long time behavior of a wave packet that is initially localized, if both nonlinearity and disorder are present.…”

“…This problem is relevant to experiments in nonlinear optics, for example disordered photonic lattices [18], where Anderson localization was found in presence of nonlinear effects as well as experiments on BECs in disordered optical lattices [19][20][21][22][23][24][25]. The interplay between disorder and nonlinear effects leads to new interesting physics [23,24,[26][27][28][29][30]. In spite of the extensive research, many fundamental problems are still open, and, in particular, it is not clear whether in one dimension (1D) Anderson localization can survive the effects of nonlinearities.…”

Discrete breathers in Josephson ladders

“…In this case chaotic localized solutions have been discovered [8]. DB have been found to play an important role in conditions far from equilibrium [9] and recently have been studied in disordered systems [10,11]. Excellent reviews on the topic are [12] and [13].…”