Energy Dynamics in a One-Dimensional Aperiodic Anharmonic Lattice

Abstract

We study the nature of collective excitations in classical anharmonic lattices with aperiodic and pseudo-random harmonic spring constants. The aperiodicity was introduced in the harmonic potential by using a sinusoidal function whose phase varies as a power-law, ϕ ∝ nν, where n labels the positions along the chain. In the absence of anharmonicity, we numerically demonstrate the existence of extended states and energy propagation for a sufficiently large degree of aperiodicity. Calculations were done by using the transfer matrix formalism (TMF), exact diagonalization and numerical solution of the Hamilton's equations. When nonlinearity is switched on, we numerically obtain a rich framework involving stable and unstable solitons.

Electron–soliton dynamics in chains with cubic nonlinearity

“…It should be noted that we are dealing with an unharmonic chain with cubic nonlinearity. Therefore, the nonlinear interaction between the nearest neighbor atoms promotes the appearance of a soliton mode [56][57][58][59][60]. The dynamics of this soliton mode is directly related to the type of nonlinearity considered and the type of initial condition chosen.…”