Obtaining Breathers in Nonlinear Hamiltonian Lattices

We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the numerical results. We discuss further applications of the method and results.Comment: 21 pages (LaTeX), 8 figures in ps-files, tar-compressed uuencoded file, Physical Review E, in pres

Breathers on lattices with long range interaction

We analyze the properties of breathers (time periodic spatially localized solutions) on chains in the presence of algebraically decaying interactions $1/r^s$. We find that the spatial decay of a breather shows a crossover from exponential (short distances) to algebraic (large distances) decay. We calculate the crossover distance as a function of $s$ and the energy of the breather. Next we show that the results on energy thresholds obtained for short range interactions remain valid for $s>3$ and that for $s < 3$ (anomalous dispersion at the band edge) nonzero thresholds occur for cases where the short range interaction system would yield zero threshold values.Comment: 4 pages, 2 figures, PRB Rapid Comm. October 199

AC-driven quantum spins: resonant enhancement of transverse DC magnetization

We consider s=1/2 spins in the presence of a constant magnetic field in z-direction and an AC magnetic field in the x-z plane. A nonzero DC magnetization component in y direction is a result of broken symmetries. A pairwise interaction between two spins is shown to resonantly increase the induced magnetization by one order of magnitude. We discuss the mechanism of this enhancement, which is due to additional avoided crossings in the level structure of the system.Comment: 7 pages, 7 figure

Interaction of discrete breathers with electrons in nonlinear lattices

We study the effects of electron-lattice interaction in the presence of discrete breathers. The lattice is treated classically. We consider two different situations - i) the scattering of an electron by a discrete breather in the semiconducting regime, where the electron-breather distance is large compared to the breather size, and ii) the appearance of a bound electron-breather state, which exists at least over one half of the breather period of oscillation. In the second case the localization length of the electron can be of the order of the breather size - a few lattice periods. Remarkably these results are derived in the absence of disorder, since discrete breathers exist in translationally invariant nonlinear lattices

Spreading of wave packets in disordered systems with tunable nonlinearity

We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^{\sigma} u_{l}$ for different values of $\sigma$. We perform extensive numerical simulations where wave packets are evolved a) without and, b) with dephasing in normal mode space. Subdiffusive spreading is observed with the second moment of wave packets growing as $t^{\alpha}$. The dependence of the numerically computed exponent $\alpha$ on $\sigma$ is in very good agreement with our theoretical predictions both for the evolution of the wave packet with and without dephasing (for $\sigma \geq 2$ in the latter case). We discuss evidence of the existence of a regime of strong chaos, and observe destruction of Anderson localization in the packet tails for small values of $\sigma$.Comment: 9 pages, 7 figure

Slow Relaxation and Phase Space Properties of a Conservative System with Many Degrees of Freedom

We study the one-dimensional discrete $\Phi^4$ model. We compare two equilibrium properties by use of molecular dynamics simulations: the Lyapunov spectrum and the time dependence of local correlation functions. Both properties imply the existence of a dynamical crossover of the system at the same temperature. This correlation holds for two rather different regimes of the system - the displacive and intermediate coupling regimes. Our results imply a deep connection between slowing down of relaxations and phase space properties of complex systems.Comment: 14 pages, LaTeX, 10 Figures available upon request (SF), Phys. Rev. E, accepted for publicatio

Resonant ratcheting of a Bose-Einstein condensate

We study the rectification process of interacting quantum particles in a periodic potential exposed to the action of an external ac driving. The breaking of spatio-temporal symmetries leads to directed motion already in the absence of interactions. A hallmark of quantum ratcheting is the appearance of resonant enhancement of the current (Europhys. Lett. 79 (2007) 10007 and Phys. Rev. A 75 (2007) 063424). Here we study the fate of these resonances within a Gross-Pitaevskii equation which describes a mean field interaction between many particles. We find, that the resonance is i) not destroyed by interactions, ii) shifting its location with increasing interaction strength. We trace the Floquet states of the linear equations into the nonlinear domain, and show that the resonance gives rise to an instability and thus to the appearance of new nonlinear Floquet states, whose transport properties differ strongly as compared to the case of noninteracting particles