Wandering breathers and self-trapping in weakly coupled nonlinear chains: classical counterpart of macroscopic tunneling quantum dynamics

TL;DR

This paper investigates the dynamics of localized excitations (breathers) in weakly coupled nonlinear chains, revealing two distinct regimes and a delocalizing transition analogous to phenomena in Bose-Einstein condensates.

Contribution

It provides analytical and numerical insights into breather behavior, including regimes of motion, bifurcations, and a delocalizing transition in 2D and 3D systems, linking classical and quantum analogies.

Findings

Identification of two dynamical regimes: immovable and wandering breathers.

Bifurcation of anti-phase two-chain breathers into single-chain breathers.

Delocalizing transition threshold depends on inter-chain coupling and amplitude.

Abstract

We present analytical and numerical studies of phase-coherent dynamics of intrinsically localized excitations (breathers) in a system of two weakly coupled nonlinear oscillator chains. We show that there are two qualitatively different dynamical regimes of the coupled breathers, either immovable or slowly-moving: the periodic transverse translation (wandering) of low-amplitude breather between the chains, and the one-chain-localization of high-amplitude breather. These two modes of coupled nonlinear excitations, which involve large number of anharmonic oscillators, can be mapped onto two solutions of a single pendulum equation, detached by a separatrix mode. We also study two-chain breathers, which can be considered as bound states of discrete breathers with different symmetry and center locations in the coupled chains, and bifurcation of the anti-phase two-chain breather into the one-chain one. Delocalizing transition of 1D breather in 2D system of a large number of parallel coupled nonlinear chains is described, in which the breather, initially excited in a given chain, abruptly spreads its vibration energy in the whole 2D system upon decreasing breather frequency or amplitude below the threshold one. The threshold breather frequency is above the cut off phonon frequency in 2D system, and the threshold breather amplitude scales as square root of the inter-chain coupling constant. Delocalizing transition of discrete vibrational breather in 2D and 3D systems of coupled nonlinear chains has an analogy with delocalizing transition for Bose-Einstein condensates in 2D and 3D optical lattices.