Andrey V. Gorbach

Discrete breathers in Fermi-Pasta-Ulam lattices

We study the properties of spatially localized and time-periodic excitations--discrete breathers--in Fermi-Pasta-Ulam (FPU) chains. We provide a detailed analysis of their spatial profiles and stability properties. We especially demonstrate that the Page mode is linearly stable for symmetric FPU potentials. A resonant interaction between a localized and delocalized perturbations causes weak but finite strength instabilities for asymmetric FPU potentials. This interaction induces Fano resonances for plane waves scattered by the breather. Finally we analyze the interplay between energy thresholds for breathers in the presence of strongly asymmetric FPU potentials and the corresponding profiles of the low-frequency limit of breather families.

Gap and out-gap breathers in a binary modulated discrete nonlinear Schrödinger model

Abstract.We consider a modulated discrete nonlinear Schrödinger (DNLS) model with alternating on-site potential, having a linear spectrum with two branches separated by a ‘forbidden’ gap. Nonlinear localized time-periodic solutions with frequencies in the gap and near the gap -- discrete gap and out-gap breathers (DGBs and DOGBs) -- are investigated. Their linear stability is studied varying the system parameters from the continuous to the anti-continuous limit, and different types of oscillatory and real instabilities are revealed. It is shown, that generally DGBs in infinite modulated DNLS chains with hard (soft) nonlinearity do not possess any oscillatory instabilities for breather frequencies in the lower (upper) half of the gap. Regimes of ‘exchange of stability’ between symmetric and antisymmetric DGBs are observed, where an increased breather mobility is expected. The transformation from DGBs to DOGBs when the breather frequency enters the linear spectrum is studied, and the general bifurcation picture for DOGBs with tails of different wave numbers is described. Close to the anti-continuous limit, the localized linear eigenmodes and their corresponding eigenfrequencies are calculated analytically for several gap/out-gap breather configurations, yielding explicit proof of their linear stability or instability close to this limit.

Optical ratchets with discrete cavity solitons.

We propose a setup to observe soliton ratchet effects using discrete cavity solitons in a 1D array of coupled waveguide optical resonators. The net motion of solitons can be generated by an adiabatic shaking of the holding beam with zero average inclination angle. The resulting soliton velocity can be controlled by different parameters of the holding beam.

Fano Resonances: A Discovery that Was Not Made 100 Years Ago

Scattering: We have missed the presence of resonant scattering behavior in the Rayleigh region for years, but a clue was lurking in quantum theory.

Resonant light scattering by optical solitons

We study the process of light scattering by optical solitons in a planar waveguide with an inhomogeneous refractive index core. A modulation of the core refractive index can be achieved by well-established techniques for producing waveguide arrays, e.g. by etching the surface of the waveguide cladding. We propose the special triple well configuration of the core, which supports resonant transmission as well as resonant reflection (Fano resonances) of light by the soliton, the latter resonance effect being a fascinating and unique property of time-periodic scattering potentials in one-dimensional systems

Classical and quantum radiation of perturbed discrete breathers

We show that the linearized phase space flow around a discrete breather solution is not capable of generating persistent energy flow away from the breather even in the case of instabilities of extended states. This holds both for the classical and quantized description of the flow. The main reason for that is the parametric driving the breather provides to the flow. Corresponding scaling arguments are derived for both classical and quantum cases. Numerical simulations of the classical flow support our findings.

Energy flow for soliton ratchets

We study the mechanism of directed energy transport for soliton ratchets. The energy flow appears due to the progressive motion of a soliton (kink) which is an energy carrier. However, the energy current formed by internal system deformations (the total field momentum) is zero. We show that the energy flow is realized via an inhomogeneous energy exchange between the system and the external ac driving. We also discuss effects of spatial discretization and combination of ac and dc external drivings.

Computational studies of discrete breathers - From basics to competing length scales

This work provides a description of the main computational tools for the study of discrete breathers. It starts with the observation of breathers through simple numerical runs, the study uses targeted initial conditions, and discrete breather impact on transient processes and thermal equilibrium. We briefly describe a set of numerical methods to obtain breathers up to machine precision. In the final part of this work we apply the discussed methods to study the competing length scales for breathers with purely anharmonic interactions — favoring superexponential localization — and long range interactions, which favor algebraic decay in space. As a result, we observe and explain the presence of three different spatial tail characteristics of the considered localized excitations.

Energy flow of moving dissipative topological solitons.

We study the energy flow due to the motion of topological solitons in nonlinear extended systems in the presence of damping and driving. The total field momentum contribution to the energy flux, which reduces the soliton motion to that of a point particle, is insufficient. We identify an additional exchange energy flux channel mediated by the spatial and temporal inhomogeneity of the system state. In the well-known case of a dc external force the corresponding exchange current is shown to be small but nonzero. For the case of ac driving forces, which lead to a soliton ratchet, the exchange energy flux mediates the complete energy flow of the system. We also consider the case of combination of ac and dc external forces, as well as spatial discretization effects.