Nonintegrable Schrodinger Discrete Breathers

In an extensive numerical investigation of nonintegrable translational motion of discrete breathers in nonlinear Schrodinger lattices, we have used a regularized Newton algorithm to continue these solutions from the limit of the integrable Ablowitz-Ladik lattice. These solutions are shown to be a superposition of a localized moving core and an excited extended state (background) to which the localized moving pulse is spatially asymptotic. The background is a linear combination of small amplitude nonlinear resonant plane waves and it plays an essential role in the energy balance governing the translational motion of the localized core. Perturbative collective variable theory predictions are critically analyzed in the light of the numerical results.Comment: 42 pages, 28 figures. to be published in CHAOS (December 2004

Intrinsically localized chaos in discrete nonlinear extended systems

The phenomenon of intrinsic localization in discrete nonlinear extended systems, i.e. the (generic) existence of discrete breathers, is shown to be not restricted to periodic solutions but it also extends to more complex (chaotic) dynamical behaviour. We illustrate this with two different forced and damped systems exhibiting this type of solutions: In an anisotropic Josephson junction ladder, we obtain intrinsically localized chaotic solutions by following periodic rotobreather solutions through a cascade of period-doubling bifurcations. In an array of forced and damped van der Pol oscillators, they are obtained by numerical continuation (path-following) methods from the uncoupled limit, where its existence is trivially ascertained, following the ideas of the anticontinuum limit.Comment: 6 pages, 6 figures, to appear in Europhysics Letter

Discrete soliton ratchets driven by biharmonic fields

Directed motion of topological solitons (kinks or antikinks) in the damped and AC-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform unidirectional motion. The phenomenon resembles the well known effects of ratchet transport and nonlinear harmonic mixing. Direction of the motion and its velocity depends on the shape of the AC drive. Necessary conditions for the occurrence of the effect are formulated. In comparison with the previously studied continuum case, the discrete case shows a number of new features: non-zero depinning threshold for the driving amplitude, locking to the rational fractions of the driving frequency, and diffusive ratchet motion in the case of weak intersite coupling.Comment: 13 pages, 13 figure

Surface spin-flop phases and bulk discommensurations in antiferromagnets

Phase diagrams as a function of anisotropy D and magnetic field H are obtained for discommensurations and surface states for a model antiferromagnet in which $H$ is parallel to the easy axis. The surface spin-flop phase exists for all $D$. We show that there is a region where the penetration length of the surface spin-flop phase diverges. Introducing a discommensuration of even length then becomes preferable to reconstructing the surface. The results are used to clarify and correct previous studies in which discommensurations have been confused with genuine surface spin-flop states.Comment: 4 pages, RevTeX, 2 Postscript figure

Quantum creep and quantum creep transitions in 1D sine-Gordan chains

Discrete sine-Gordon (SG) chains are studied with path-integral molecular dynamics. Chains commensurate with the substrate show the transition from collective quantum creep to pinning at bead masses slightly larger than those predicted from the continuous SG model. Within the creep regime, a field-driven transition from creep to complete depinning is identified. The effects of disorder in the external potential on the chain's dynamics depend on the potential's roughness exponent $H$, i.e., quantum and classical fluctuations affect the current self-correlation functions differently for $H = 1/2$.Comment: 4 pages, 3 figure

An Upsilon Point in a Spin Model

We present analytic evidence for the occurrence of an upsilon point, an infinite checkerboard structure of modulated phases, in the ground state of a spin model. The structure of the upsilon point is studied by calculating interface--interface interactions using an expansion in inverse spin anisotropy.Comment: 18 pages ReVTeX file, including 6 figures encoded with uufile

Resonant steps and spatiotemporal dynamics in the damped dc-driven Frenkel-Kontorova chain

Kink dynamics of the damped Frenkel-Kontorova (discrete sine-Gordon) chain driven by a constant external force are investigated. Resonant steplike transitions of the average velocity occur due to the competitions between the moving kinks and their radiated phasonlike modes. A mean-field consideration is introduced to give a precise prediction of the resonant steps. Slip-stick motion and spatiotemporal dynamics on those resonant steps are discussed. Our results can be applied to studies of the fluxon dynamics of 1D Josephson-junction arrays and ladders, dislocations, tribology and other fields.Comment: 20 Plain Latex pages, 10 Eps figures, to appear in Phys. Rev.

Surface spin-flop and discommensuration transitions in antiferromagnets

Phase diagrams as a function of anisotropy $D$ and magnetic field $H$ are obtained for discommensurations and surface states for an antiferromagnet in which $H$ is parallel to the easy axis, by modeling it using the ground states of a one-dimensional chain of classical XY spins. A surface spin-flop phase exists for all $D$, but the interval in $H$ over which it is stable becomes extremely small as $D$ goes to zero. First-order transitions, separating different surface states and ending in critical points, exist inside the surface spin-flop region. They accumulate at a field $H'$ (depending on $D$) significantly less than the value $H_{SF}$ for a bulk spin-flop transition. For $H' < H < H_{SF}$ there is no surface spin-flop phase in the strict sense; instead, the surface restructures by, in effect, producing a discommensuration infinitely far away in the bulk. The results are used to explain in detail the phase transitions occurring in systems consisting of a finite, even number of layers.Comment: Revtex 17 pages, 15 figure