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.

We study the dynamics of skyrmions in Dzyaloshinskii-Moriya materials with easy-axis anisotropy. An important link between topology and dynamics is established through the construction of unambiguous conservation laws obtained earlier in connection with magnetic bubbles and vortices. In particular, we study the motion of a topological skyrmion with skyrmion number Q = 1 and a non-topological skyrmionium with Q = 0 under the influence of an applied field gradient. The Q = 1 skyrmion undergoes Hall motion perpendicular to the direction of the field gradient with a drift velocity proportional to the gradient. In contrast, the non-topological Q = 0 skyrmionium is accelerated in the direction of the field gradient, thus exhibiting ordinary Newtonian motion. When the applied field is switched off the Q = 1 skyrmion is spontaneously pinned around a fixed guiding center, whereas the Q = 0 skyrmionium moves with constant velocity v. We give a systematic calculation of a skyrmionium traveling with any constant velocity v that is smaller than a critical velocity vc.

We study numerically the dynamics of a magnetic bubble in a disc-shaped magnetic element which is probed by a pulse of a magnetic field gradient. Magnetic bubbles are nontrivial magnetic configurations which are characterized by a topological (skyrmion) number N and they have been observed in mesoscopic magnetic elements with strong perpendicular anisotropy. For weak fields we find a skew deflection of the axially symmetric N = 1 bubble and a subsequent periodic motion around the center of the dot. This gyrotropic motion of the magnetic bubble is shown here for the first time. Stronger fields induce switching of the N = 1 bubble to a bubble which contains a pair of Bloch lines and has N = 0. The N = 0 bubble can be switched back to a N = 1 bubble by applying again an external field gradient. Detailed features of the unusual bubble dynamics are described by employing the skyrmion number and the moments of the associated topological density.

We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schrödinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization length (Anderson localization). Nonlinear terms in the equations of motion destroy the Anderson localization due to nonintegrability and deterministic chaos. At least a finite part of an initially localized wave packet will subdiffusively spread without limits. We analyze the details of this spreading process. We compare the evolution of single-site, single-mode, and general finite-size excitations and study the statistics of detrapping times. We investigate the properties of mode-mode resonances, which are responsible for the incoherent delocalization process.

A direct link between the topological complexity of ferromagnetic media and their dynamics has recently been established through the construction of unambiguous conservation laws as moments of a topological vorticity. In the present paper we carry out this program under completely realistic conditions, with due account of the long-range magnetostatic field and related boundary effects. In particular, we derive unambiguous expressions for the linear and angular momentum in a ferromagnetic film which are then used to study the dynamics of magnetic bubbles under the influence of an applied magnetic-field gradient. The semi-empirical golden rule of bubble dynamics is verified in its gross features but not in its finer details. A byproduct of our analysis is a set of virial theorems generalizing Derrick's scaling relation as well as a detailed recalculation of the fundamental magnetic bubble.1

We investigate propagation of a charge carrier along intrinsically dynamically disordered double-stranded DNA. This is realized by the semiclassical coupling of the charge with a nonlinear lattice model that can accurately describe the statistical mechanics of the large amplitude fluctuations of the base pairs leading to the thermal denaturation transition of DNA. We find that the fluctuating intrinsic disorder can trap the charge and inhibit polaronic charge transport. The dependence of the mean distance covered by the charge carrier until its trapping, as a function of the energy of the fluctuations of the base pairs is also presented.

We present the results of numerical calculations of the groundstates of weakly-interacting BoseEinstein condensates containing large numbers of vortices. Our calculations show that these groundstates appear to be close to uniform triangular vortex lattices. However, slight deviations from a uniform triangular lattice have dramatic consequences on the overall particle distribution. In particular, we demonstrate that the overall particle distribution averaged on a lengthscale large compared to the vortex lattice constant is well approximated by a Thomas-Fermi profile.

Quasi-one-dimensional solitons that may occur in an elongated Bose-Einstein condensate become unstable at high particle density. We study two basic modes of instability and the corresponding bifurcations to genuinely three-dimensional solitary waves such as axisymmetric vortex rings and non-axisymmetric solitonic vortices. We calculate the profiles of the above structures and examine their dependence on the velocity of propagation along a cylindrical trap. At sufficiently high velocity, both the vortex ring and the solitonic vortex transform into an axisymmetric soliton. We also calculate the energy-momentum dispersions and show that a Lieb-type mode appears in the excitation spectrum for all particle densities.