RESUMEN
We study the spreading of an initially localized wave packet in two nonlinear chains (discrete nonlinear Schrödinger and quartic Klein-Gordon) with disorder. Previous studies suggest that there are many initial conditions such that the second moment of the norm and energy density distributions diverges with time. We find that the participation number of a wave packet does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times we find a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wave packet, we rule out the possibility of slow energy diffusion. The dynamical state could approach a quasiperiodic solution (Kolmogorov-Arnold-Moser torus) in the long time limit.
RESUMEN
We propose a simple, novel mechanism for inducing highly selective and efficient energy transfer and focusing in certain discrete nonlinear systems. Under a precise condition of nonlinear resonance, when a specific amount of energy is injected as a discrete breather at a donor system, it can be transferred as a discrete breather to another weakly coupled acceptor system. This general mechanism could be relevant for energy transfer in bioenergetics and electron transfer in chemical reactions and could be used for engineering functional materials and devices.
RESUMEN
We find exact localized time-periodic solutions with frequencies inside the linearized spectrum [intraband discrete breathers (IDBs)] in random nonlinear models using a new self-consistent method. The IDB frequencies belong to intervals between forbidden gaps generated by resonances with the linear modes, becoming fat Cantor sets in infinite systems. When localized IDBs are continued versus frequency, they delocalize and become multisite IDBs (not predicted by existing theorems), which can propagate energy. Some implications for energy relaxation in glasses are discussed.
RESUMEN
In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal 0,pi. Incommensurate analytic SWs with |Q|>pi/2 may however appear as "quasistable," as their instability growth rate is of higher order.