Interference effects in soliton scattering by impurities

Abstract

Abstract. We present a comprehensive study ofthe effects of inhomogeneities on nonlinear excitation dynamics in different one-dimensional soliton-bearing systems. We theoretically analyse soliton scattering by one and two point-like impurities in the framework of the predict that interference effects arise in the form of an oscillatory dependence ofthe soliton reflection coefficient on the distance between impurities. The main fanor responsible for this behaviour is the spectral density of the soliton radiation: the values of that distance which are integer multiples of the main wavelength radiated by the soliton upon collision with the inhomogeneities give rise to resonant scattering, with very link reflection. Our approximate analytical predictions explain previous numerical results concerning nonlinear lattices, and are further supported by new simulations that we have performed on.thc sine-Gordon system.

Enhanced fluxon transmission through impurities

“…The resonant transmission does not occur if the fluxon interacts with two impurities of different sign: a microshort and a microresistor. The observed effect should not be confused with the resonant soliton transmission in the non-dissipative cases [5,6]. In the case of fluxon dynamics in a long Josephson junction the presence of dissipation is unavoidable.…”

“…A natural question arises: what is an analog of the quantum-mechanical resonant tunneling in the fluxon dynamics? Resonant soliton transmission has been investigated in detail for nondissipative systems [5,6] and complex resonant behaviour has been reported. However, fluxon dynamics in a LJJ cannot be considered without taking into account dissipative effects, which are a consequence of the normal electron tunneling across the insulating barrier.…”

Ratchet behavior in nonlinear Klein-Gordon systems with pointlike inhomogeneities

“…In addition, as in the sG model we will have dynamical changes of the effective potential due to the kink width variations, making more complicated the dynamics of motion. In any event, these effective potentials obtained in the simple approach highlight the importance of interference effects (see also [23,28]) and make it clear that the kink width is not the unique quantity to take into account.…”

“…This is an intrinsic feature of these nonlinear excitations, and correspondingly the competition between their width and the distances among the inhomogeneities is crucial for the kink motion. The interference effects among the inhomogeneities [28] create an effective potential for the motion of the kink center, the location of the inhomogeneities determining the direction of motion. For the particular configuration of three inhomogeneities per unit cell, directional motion takes place only under the condition a = b.…”

“…Another relevant conclusion is the feedback between the effective potential landscape and the kink width, determined in turn by the potential. In this fashion, the 2-CC approach reflects the non-trivial interaction of the kink with the inhomogeneities, which is otherwise known to exhibit many counterintuitive phenomena [28].…”