5,038 research outputs found
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 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, , 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 , and with the existence of the
magnetic field at the scale G between the neutrinosphere and the
shock-wave stagnation region, it is shown that an additional energy of the
order of 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,
, and the wave group velocity, . 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
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