Chiral Skyrmionic matter in non-centrosymmetric magnets

Axisymmetric magnetic strings with a fixed sense of rotation and nanometer sizes (chiral magnetic vortices or Skyrmions) have been predicted to exist in a large group of non-centrosymmetric crystals more than two decades ago. Recently these extraordinary magnetic states have been directly observed in thin layers of cubic helimagnet (Fe,Co)Si. In this report we apply our earlier theoretical findings to review main properties of chiral Skyrmions, to elucidate their physical nature, and to analyse these recent experimental results on magnetic-field-driven evolution of Skyrmions and helicoids in chiral helimagnets.Comment: 13 pages, 7 figures, invited talk - JEMS-2010 ( 23-28 August, Krakow, Poland

Solutions for real dispersionless Veselov-Novikov hierarchy

We investigate the dispersionless Veselov-Novikov (dVN) equation based on the framework of dispersionless two-component BKP hierarchy. Symmetry constraints for real dVN system are considered. It is shown that under symmetry reductions, the conserved densities are therefore related to the associated Faber polynomials and can be solved recursively. Moreover, the method of hodograph transformation as well as the expressions of Faber polynomials are used to find exact real solutions of the dVN hierarchy.Comment: 14 page

Probability of radiation of twisted photons by classical currents

The general formula for the probability of radiation of a twisted photon by a classical current is derived. The general theory of generation of twisted photons by undulators is developed. It is proved that the probability to record a twisted photon produced by a classical current is equal to the average number of twisted photons in a given state. The general formula for the projection of the total angular momentum of twisted photons with given the energy, the longitudinal projection of momentum, and the helicity is obtained. The symmetry property of the average number of twisted photons produced by a charged particle moving along a planar trajectory is found. The explicit formulas for the average number of twisted photons generated by undulators both in the dipole and wiggler regimes are obtained. It is established that, for the forward radiation of an ideal right-handed helical undulator, the harmonic number $n$ of the twisted photon coincides with its projection of the total angular momentum $m$. As for the ideal left-handed helical undulator, we obtain that $m=-n$. It is found that the forward radiation of twisted photons by a planar undulator obeys the selection rule that $n+m$ is an even number. It turns out that the average number of twisted photons produced by the undulator and detected off the undulator axis is a periodic function of $m$ in a certain spectral band of the quantum numbers $m$.Comment: 36 pp; some misprints corrected; formulas (48)-(51) change

Properties of an ultrarelativistic charged particle radiation in a constant homogeneous crossed electromagnetic field

The properties of radiation created by a classical ultrarelativistic scalar charged particle in a constant homogeneous crossed electromagnetic field are described both analytically and numerically with radiation reaction taken into account in the form of the Landau-Lifshitz equation. The total radiation naturally falls into two parts: the radiation formed at the entrance point of a particle into the crossed field (the synchrotron entrance radiation), and the radiation coming from the late-time asymptotics of a particle motion (the de-excited radiation). The synchrotron entrance radiation resembles, although does not coincide with, the ultrarelativistic limit of the synchrotron radiation: its distribution over energies and angles possesses almost the same properties. The de-excited radiation is soft, not concentrated in the plane of motion of a charged particle, and almost completely circularly polarized. The photon energy delivering the maximum to its spectral angular distribution decreases with increasing the initial energy of a charged particle, while the maximum value of this distribution remains the same at the fixed observation angle. The ultraviolet and infrared asymptotics of the total radiation are also described.Comment: 14 pp, 3 fig

On the heavenly equation hierarchy and its reductions

Second heavenly equation hierarchy is considered using the framework of hyper-K\"ahler hierarchy developed by Takasaki. Generating equations for the hierarchy are introduced, they are used to construct generating equations for reduced hierarchies. General $N$-reductions, logarithmic reduction and rational reduction for one of the Lax-Sato functions are discussed. It is demonstrated that rational reduction is equivalent to the symmetry constraint.Comment: 13 pages, LaTeX, minor misprints corrected, references adde