Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal

Abstract

We investigate a two-dimensional ͑2D͒ strongly anisotropic crystal ͑2D SAC͒ on substrate: 2D system of coupled linear chains of particles with strong intrachain and weak interchain interactions, each chain being subjected to the sine background potential. Nonlinear dynamics of one of these chains when the rest of them are fixed is reduced to the well known Frenkel-Kontorova ͑FK͒ model. Depending on strengh of the substrate, the 2D SAC models a variety of physical systems: polymer crystals with identical chains having light side groups, an array of inductively coupled long Josephson junctions, anisotropic crystals having light and heavy sublattices. Continuum limit of the FK model, the sine-Gordon ͑sG͒ equation, allows two types of soliton solutions: topological solitons and breathers. It is known that the quasi-one-dimensional topological solitons can propagate also in a chain of 2D system of coupled chains and even in a helix chain in a three-dimensional model of polymer crystal. In contrast to this, numerical simulation shows that the long-living breathers inherent to the FK model do not exist in the 2D SAC with weak background potential. The effect changes scenario of kink-antikink collision with small relative velocity: at weak background potential the collision always results only in intensive phonon radiation while kink-antikink recombination in the FK model results in long-living low-frequency sG breather creation. We found the survival condition for breathers in the 2D SAC on substrate depending on breather frequency and strength of the background potential. The survival condition bears no relation to resonances between breather frequency and frequencies of phonon band-contrary to the case of the FK model.

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

“…Torsion dynamics of DNA double helix can also be approximated by the β-FPU Hamiltonian (1) [24]. On the other hand, weakly coupled nonlinear molecular chains in polymers are characterized by the asymmetric intra-chain anharmonic potential, with nonzero α (i) [25,26].…”

“…( 22) and ( 23), but does not enter evolution equations ( 25) and ( 26) for Θ and Φ. Equations similar to Eqs. ( 25) and (26) were probably derived for the first time in Ref. [41] for the description of energy exchange between two weakly coupled classical anharmonic oscillators (with ω m1 = ω m2 and α = 0).…”

“…Recent experiments have demonstrated the existence of intrinsically localized modes and breathers in various systems such as 2D and 3D arrays of nonlinear optical waveguides [11,12], low-dimensional crystals [13], antiferromagnetic materials [14], Josephson junction arrays [15], photonic structures and micromechanical systems [17], protein α-helices [18], and α-uranium [19]. Slowlymoving breathers and supersonic kink-solitons were also described in 1D nonlinear chains [6,7,20,21,22,23], DNA macromolecules [24] and quasi-1D polymer crystals [25,26].…”

Simulation of Epitaxial Film–Substrate Interaction Potential

“…The cosine function specifies the periodic substrate potential. This simple approximation reveals a wide variety of ground states for the system [4][5][6] and different waves in the atoms chain [7][8][9]. Solitons are of the greatest interest.…”

Extended class of exact twistons and crystalline polyethylene

“…The twist occurs along the plane which is orthogonal to the chain direction. In fact, there are several works discussing a number of solitonic models in crystalline polyethylene [2][3][4][5][6], as well as other types of organic chains [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”