On the internal modes in sine-Gordon chain

We address the issue of internal modes of a kink of a discrete sine-Gordon equation. The main point of the present study is to elucidate how the antisymmetric internal mode frequency dependence enters the quasicontinuum spectrum of nonlocalized waves. We analyze the internal frequency dependencies as functions of both the number of cites and discreteness parameter and explain the origin of spectrum peculiarity which arises after the frequency dependence of antisymmetric mode returns back to the continuous spectrum at some nonzero value of the intersite coupling.Comment: 5 pages, 3 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

Group analysis and renormgroup symmetries

An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries, based on modern group analysis are described. Application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.Comment: 17 pages, RevTeX LATeX file, to appear in Journal of Mathematical Physic

Aharonov-Casher effect in a two dimensional hole gas with spin-orbit interaction

We study the quantum interference effects induced by the Aharonov-Casher phase in a ring structure in a two-dimensional heavy hole (HH) system with spin-orbit interaction realizable in narrow asymmetric quantum wells. The influence of the spin-orbit interaction strength on the transport is investigated analytically. These analytical results allow us to explain the interference effects as a signature of the Aharonov-Casher Berry phases. Unlike previous studies on the electron two-dimensional Rashba systems, we find that the frequency of conductance modulations as a function of the spin-orbit strength is not constant but increases for larger spin-orbit splittings. In the limit of thin channel rings (width smaller than Fermi wavelength), we find that the spin-orbit splitting can be greatly increased due to quantization in the radial direction. We also study the influence of magnetic field considering both limits of small and large Zeeman splittings.Comment: 6 pages, 4 figure

Observational evidence for the origin of high-energy neutrinos in parsec-scale nuclei of radio-bright active galaxies

Observational information on high-energy astrophysical neutrinos is being continuously collected by the IceCube observatory. However, the sources of neutrinos are still unknown. In this study, we use radio very-long-baseline interferometry (VLBI) data for a complete VLBI-flux-density limited sample of active galactic nuclei (AGN). We address the problem of the origin of astrophysical neutrinos with energies above 200 TeV in a statistical manner. It is found that AGN positionally associated with IceCube events have typically stronger parsec-scale cores than the rest of the sample. The post-trial probability of a chance coincidence is 0.2%. We select the four strongest AGN as highly probable associations: 3C 279, NRAO 530, PKS 1741-038, and PKS 2145+067. Moreover, we find an increase of radio emission at frequencies above 10 GHz around neutrino arrival times for several other VLBI-selected AGN on the basis of RATAN-600 monitoring. The most pronounced example of such behavior is PKS 1502+106. We conclude that AGN with bright Doppler-boosted jets constitute an important population of neutrino sources. High-energy neutrinos are produced in their central parsec-scale regions, probably in proton-photon interactions at or around the accretion disk. Radio-bright AGN that are likely associated with neutrinos have very diverse gamma-ray properties suggesting that gamma-rays and neutrinos may be produced in different regions of AGN and not directly related. A small viewing angle of the jet-disk axis is, however, required to detect either of them.Comment: 19 pages, 5 figures, 3 tables; accepted to ApJ; v2: extended discussion, added a figure and electronic table; v3: fixed typo in a source nam