Plasma induced neutrino radiative decay instead of neutrino spin light

The conversion nu_L -> nu_R gamma^* of a neutrino with a magnetic moment is considered, caused by the additional Wolfenstein energy acquired by a left-handed neutrino in medium, with an accurate taking account of the photon \gamma^* dispersion in medium. It is shown that the threshold arises in the process, caused by the photon (plasmon) effective mass. This threshold leaves no room for the so-called "neutrino spin light" in the most of astrophysical situations.Comment: 7 pages, LaTeX, 1 EPS figure, submitted to Modern Physics Letters

Backlund transformations for the sl(2) Gaudin magnet

Elementary, one- and two-point, Backlund transformations are constructed for the generic case of the sl(2) Gaudin magnet. The spectrality property is used to construct these explicitly given, Poisson integrable maps which are time-discretizations of the continuous flows with any Hamiltonian from the spectral curve of the 2x2 Lax matrix.Comment: 17 pages, LaTeX, refs adde

Backlund transformations for many-body systems related to KdV

We present Backlund transformations (BTs) with parameter for certain classical integrable n-body systems, namely the many-body generalised Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the fact that all these systems may be obtained as particular reductions (stationary or restricted flows) of the KdV hierarchy; alternatively they may be considered as examples of the reduced sl(2) Gaudin magnet. The BTs provide exact time-discretizations of the original (continuous) systems, preserving the Lax matrix and hence all integrals of motion, and satisfy the spectrality property with respect to the Backlund parameter.Comment: LaTeX2e, 8 page

Relaxation of nonlinear oscillations in BCS superconductivity

The diagonal case of the $sl(2)$ Richardson-Gaudin quantum pairing model \cite{Richardson1,Richardson2,Richardson3,Richardson4,Richardson5,Richardson6,G audin76} is known to be solvable as an Abel-Jacobi inversion problem \cite{SOV,Kuznetzov,Kuz1,Kuz2,Kuz3,Kuz4,Kuz5,YAKE04}. This is an isospectral (stationary) solution to a more general integrable hierarchy, in which the full time evolution can be written as isomonodromic deformations. Physically, the more general solution is appropriate when the single-particle electronic spectrum is subject to external perturbations. The asymptotic behavior of the nonlinear oscillations in the case of elliptic solutions is derived

Baxter's Q-operator for the homogeneous XXX spin chain

Applying the Pasquier-Gaudin procedure we construct the Baxter's Q-operator for the homogeneous XXX model as integral operator in standard representation of SL(2). The connection between Q-operator and local Hamiltonians is discussed. It is shown that operator of Lipatov's duality symmetry arises naturally as leading term of the asymptotic expansion of Q-operator for large values of spectral parameter.Comment: 23 pages, Late

Dirac neutrino magnetic moment and the shock wave revival in a supernova explosion

The process of the two-step conversion of the neutrino helicity, $\nu_L \to \nu_R \to \nu_L$, is analysed in the supernova conditions, where the first stage is realized due to the interaction of the neutrino magnetic moment with the plasma electrons and protons in the supernova core. The second stage is caused by the neutrino resonant spin-flip in a magnetic field of the supernova envelope. Given the neutrino magnetic moment within the interval $10^{-13} \mu_{\rm B} < \mu_\nu < 10^{-12} \mu_{\rm B}$, and with the existence of the magnetic field at the scale $\sim 10^{13}$ G between the neutrinosphere and the shock-wave stagnation region, it is shown that an additional energy of the order of $10^{51}$ erg can be injected into this region during the typical time of the shock-wave stagnation. This energy could be sufficient for stumulation of the damped shock wave.Comment: 6 pages, LaTeX, 2 PS figures, based on the talk presented by N.V. Mikheev at the XV International Seminar Quarks'2008, Sergiev Posad, Moscow Region, May 23-29, 2008, to appear in the Proceeding

Separation of variables for A2 Ruijsenaars model and new integral representation for A2 Macdonald polynomials

Using the Baker-Akhiezer function technique we construct a separation of variables for the classical trigonometric 3-particle Ruijsenaars model (relativistic generalization of Calogero-Moser-Sutherland model). In the quantum case, an integral operator M is constructed from the Askey-Wilson contour integral. The operator M transforms the eigenfunctions of the commuting Hamiltonians (Macdonald polynomials for the root sytem A2) into the factorized form S(y1)S(y2) where S(y) is a Laurent polynomial of one variable expressed in terms of the 3phi2(y) basic hypergeometric series. The inversion of M produces a new integral representation for the A2 Macdonald polynomials. We also present some results and conjectures for general n-particle case.Comment: 31 pages, latex, no figures, Proposition 12 correcte

Triggering rogue waves in opposing currents

We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity, $U_0$, and the wave group velocity, $c_g$. We also reveal that an opposing current can force the development of rogue waves in random wave fields, resulting in a substantial change of the statistical properties of the surface elevation. The present results can be directly adopted in any field of physics in which the focusing Nonlinear Schrodinger equation with non constant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.Comment: 5 pages, 5 figure

Evolution of rarefaction pulses into vortex rings

The two-dimensional solitary waves of the Gross-Pitaevskii equation in the Kadomtsev-Petviashvili limit are unstable with respect to three-dimensional perturbations. We elucidate the stages in the evolution of such solutions subject to perturbations perpendicular to the direction of motion. Depending on the energy (momentum) and the wavelength of the perturbation different types of three-dimensional solutions emerge. In particular, we present new periodic solutions having very small energy and momentum per period. These solutions also become unstable and this secondary instability leads to vortex ring nucleation.Comment: 5 pages, 5 figure