Driven dynamics: a photodriven Frenkel-Kontorova model

Breathers in a nonautonomous Toda lattice with pulsating coupling

We study a nonautonomous Toda lattice, with a periodically switched on-off coupling coefficient, describing a pulsating strength of neighbor particle interaction. It is shown that when the uncoupled oscillations are linear and under appropriate conditions for the duration of the time intervals where the coupling is switched off, breather solutions can be obtained analytically. Their dynamics and collisions are related to the soliton dynamics of the corresponding autonomous Toda lattice, while a "ratchet" effect is shown to result in breather deceleration, providing a mechanism for breather velocity and collision control.

Nonlinear constructive interference in electrical lattices

We analyze the constructive interference of input signals in nonlinear, discrete, two-dimensional media. The media consist of inductor-capacitor lattices with saturating, voltage-dependent capacitors. We find that nonlinearity significantly boosts the ability of such media to generate large-amplitude output signals from small-amplitude inputs. To understand this boosting, we develop a general perturbative method suitable for finding the steady-state solution of a damped NxN nonlinear lattice that is driven at a single frequency. We verify our theory using extensive numerical simulations.

Collective directed transport of symmetrically coupled lattices in symmetric periodic potentials

A mechanism responsible for the directed transport of symmetrically coupled lattices in a symmetric periodic potential is proposed. Under the action of an external wave that breaks the spatiotemporal symmetry and introduces inhomogeneities of the lattice, a net unidirectional current can be observed, originating from a collaboration of the lattice (periodic potential and mutual interactions) and the wave (amplitude, frequency, and phase shifts). Mode-locking induced resonant steps are observed and predicted. The directed transport can be optimized and furthermore controlled by suitably adjusting the parameters of the system.