Soliton dynamics in damped and forced Boussinesq equations

We investigate the dynamics of a lattice soliton on a monatomic chain in the presence of damping and external forces. We consider Stokes and hydrodynamical damping. In the quasi-continuum limit the discrete system leads to a damped and forced Boussinesq equation. By using a multiple-scale perturbation expansion up to second order in the framework of the quasi-continuum approach we derive a general expression for the first-order velocity correction which improves previous results. We compare the soliton position and shape predicted by the theory with simulations carried out on the level of the monatomic chain system as well as on the level of the quasi-continuum limit system. For this purpose we restrict ourselves to specific examples, namely potentials with cubic and quartic anharmonicities as well as the truncated Morse potential, without taking into account external forces. For both types of damping we find a good agreement with the numerical simulations both for the soliton position and for the tail which appears at the rear of the soliton. Moreover we clarify why the quasi-continuum approximation is better in the hydrodynamical damping case than in the Stokes damping case

Long-range effects on superdiffusive solitons in anharmonic chains

Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam (FPU)-like lattices were recently generalized to the case of dispersive long-range interactions (LRI) of the Kac-Baker form. The position variance of the soliton shows a stronger than linear time-dependence (superdiffusion) as found earlier for lattice solitons on FPU chains with nearest neighbour interactions (NNI). In contrast to the NNI case where the position variance at moderate soliton velocities has a considerable linear time-dependence (normal diffusion), the solitons with LRI are dominated by a superdiffusive mechanism where the position variance mainly depends quadratic and cubic on time. Since the superdiffusion seems to be generic for nontopological solitons, we want to illuminate the role of the soliton shape on the superdiffusive mechanism. Therefore, we concentrate on a FPU-like lattice with a certain class of power-law long-range interactions where the solitons have algebraic tails instead of exponential tails in the case of FPU-type interactions (with or without Kac-Baker LRI). A collective variable (CV) approach in the continuum approximation of the system leads to stochastic integro-differential equations which can be reduced to Langevin-type equations for the CV position and width. We are able to derive an analytical result for the soliton diffusion which agrees well with the simulations of the discrete system. Despite of structurally similar Langevin systems for the two soliton types, the algebraic solitons reach the superdiffusive long-time limit with a characteristic $t^{1.5}$ time-dependence much faster than exponential solitons. The soliton shape determines the diffusion constant in the long-time limit that is approximately a factor of $\pi$ smaller for algebraic solitons.Comment: 7 figure

Scattering of vortex pairs in 2D easy-plane ferromagnets

Vortex-antivortex pairs in 2D easy-plane ferromagnets have characteristics of solitons in two dimensions. We investigate numerically and analytically the dynamics of such vortex pairs. In particular we simulate numerically the head-on collision of two pairs with different velocities for a wide range of the total linear momentum of the system. If the momentum difference of the two pairs is small, the vortices exchange partners, scatter at an angle depending on this difference, and form two new identical pairs. If it is large, the pairs pass through each other without losing their identity. We also study head-tail collisions. Two identical pairs moving in the same direction are bound into a moving quadrupole in which the two vortices as well as the two antivortices rotate around each other. We study the scattering processes also analytically in the frame of a collective variable theory, where the equations of motion for a system of four vortices constitute an integrable system. The features of the different collision scenarios are fully reproduced by the theory. We finally compare some aspects of the present soliton scattering with the corresponding situation in one dimension.Comment: 13 pages (RevTeX), 8 figure

Speed-of-light pulses in a nonlinear Weyl equation

We introduce a prototypical nonlinear Weyl equation, motivated by recent developments in massless Dirac fermions, topological semimetals and photonics. We study the dynamics of its pulse solutions and find that a localized one-hump initial condition splits into a localized two-hump pulse, while an associated phase structure emerges in suitable components of the spinor field. For times larger than a transient time $t_s$ this pulse moves with the speed of light (or Fermi velocity in Weyl semimetals), effectively featuring linear wave dynamics and maintaining its shape (both in two and three dimensions). We show that for the considered nonlinearity, this pulse represents an exact solution of the nonlinear Weyl (NLW) equation. Finally, we comment on the generalization of the results to a broader class of nonlinearities and on their emerging potential for observation in different areas of application.Comment: 7 pages, 6 figure

Modeling of electron emission processes accompanying Radon-α\alpha-decays within electrostatic spectrometers

Electrostatic spectrometers utilized in high-resolution beta-spectroscopy studies such as in the Karlsruhe Tritium Neutrino (KATRIN) experiment have to operate with a background level of less than 10^(-2) counts per second. This limit can be exceeded by even a small number of Rn-219 or Rn-220 atoms being emanated into the volume and undergoing alpha-decay there. In this paper we present a detailed model of the underlying background-generating processes via electron emission by internal conversion, shake-off and relaxation processes in the atomic shells of the Po-215 and Po-216 daughters. The model yields electron energy spectra up to 400 keV and electron multiplicities of up to 20 which are compared to experimental data.Comment: 7 figure

Controlled vortex core switching in a magnetic nanodisk by a rotating field

The switching process of the vortex core in a Permalloy nanodisk affected by a rotating magnetic field is studied theoretically. A detailed description of magnetization dynamics is obtained by micromagnetic simulations.Comment: REVTeX, 5 pages, 5 figure

Noise-induced switching between vortex states with different polarization in classical two-dimensional easy-plane magnets

In the 2-dimensional anisotropic Heisenberg model with XY-symmetry there are non-planar vortices which exhibit a localized structure of the z-components of the spins around the vortex center. We study how thermal noise induces a transition of this structure from one polarization to the opposite one. We describe the vortex core by a discrete Hamiltonian and consider a stationary solution of the Fokker-Planck equation. We find a bimodal distribution function and calculate the transition rate using Langer's instanton theory (1969). The result is compared with Langevin dynamics simulations for the full many-spin model.Comment: 15 pages, 4 figures, Phys. Rev. B., in pres

Switching between different vortex states in 2-dimensional easy-plane magnets due to an ac magnetic field

Using a discrete model of 2-dimensional easy-plane classical ferromagnets, we propose that a rotating magnetic field in the easy plane can switch a vortex from one polarization to the opposite one if the amplitude exceeds a threshold value, but the backward process does not occur. Such switches are indeed observed in computer simulations.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let