355 research outputs found
Classification of electromagnetic resonances in finite inhomogeneous three-dimensional structures
We present a simple and unified classification of macroscopic electromagnetic
resonances in finite arbitrarily inhomogeneous isotropic dielectric 3D
structures situated in free space. By observing the complex-plane dynamics of
the spatial spectrum of the volume integral operator as a function of angular
frequency and constitutive parameters we identify and generalize all the usual
resonances, including complex plasmons, real laser resonances in media with
gain, and real quasi-static resonances in media with negative permittivity and
gain.Comment: 4 pages, 2 figure
Correlations among elastic and inelastic cross-sections and slope parameter
We discuss the unitarity motivated relations among the elastic cross-section,
slope parameter and inelastic cross-section of the high energy \textit{pp}
interaction. In particular, the MacDowell-Martin unitarity bound is written
down in another form to make a relation between the elastic and inelastic
quantities more transparent. On the basis of an unitarity motivated relation we
argue that the growth with energy of the elastic to total cross-section ratio
is a consequence of the increasing with energy of the \textit{inelastic
interaction intensity}. The latter circumstance is an underlying reason for the
acceleration of the slope parameter growth, for the slowing of the growth of
the elastic to total cross-section ratio and for other interesting phenomena,
which are observed in the TeV energy range. All of this confirms the old idea
that the elastic scattering is a shadow of the particle production processes.Comment: 16 pages, 6 figure
Classical phase fluctuations in d-wave superconductors
We study the effects of low-energy nodal quasiparticles on the classical
phase fluctuations in a two-dimensional d-wave superconductor. The
singularities of the phase-only action at T\to 0 are removed in the presence of
disorder, which justifies using an extended classical XY-model to describe
phase fluctuations at low temperatures.Comment: 14 pages, brief review for Mod. Phys. Lett.
Coexistence of Ferromagnetism and Superconductivity in Noncentrosymmetric Materials with Cubic Symmetry
This is a model study for the emergence of superconductivity in
ferromagnetically ordered phases of cubic materials whose crystal structure
lacks inversion symmetry. A Ginzburg-Landau-type theory is used to find the
ferromagnetic state and to determine the coupling of magnetic order to
superconductivity. It is found that noncentrosymmetricity evokes a helical
magnetic phase. If the wavelength of the magnetic order is long enough, it
gives rise to modulations of the order parameter of superconductivity, both in
modulus and complex phase. At magnetic domain walls the nucleation of
superconductivity is found to be suppressed as compared to the interior of
ferromagnetic domains.Comment: 5 pages, 2 figure
On the classification of conditionally integrable evolution systems in (1+1) dimensions
We generalize earlier results of Fokas and Liu and find all locally analytic
(1+1)-dimensional evolution equations of order that admit an -shock type
solution with .
To this end we develop a refinement of the technique from our earlier work
(A. Sergyeyev, J. Phys. A: Math. Gen, 35 (2002), 7653--7660), where we
completely characterized all (1+1)-dimensional evolution systems
\bi{u}_t=\bi{F}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^n\bi{u}/\p x^n) that are
conditionally invariant under a given generalized (Lie--B\"acklund) vector
field \bi{Q}(x,t,\bi{u},\p\bi{u}/\p x,...,\p^k\bi{u}/\p x^k)\p/\p\bi{u} under
the assumption that the system of ODEs \bi{Q}=0 is totally nondegenerate.
Every such conditionally invariant evolution system admits a reduction to a
system of ODEs in , thus being a nonlinear counterpart to quasi-exactly
solvable models in quantum mechanics.
Keywords: Exact solutions, nonlinear evolution equations, conditional
integrability, generalized symmetries, reduction, generalized conditional
symmetries
MSC 2000: 35A30, 35G25, 81U15, 35N10, 37K35, 58J70, 58J72, 34A34Comment: 8 pages, LaTeX 2e, now uses hyperre
Singular Modes of the Electromagnetic Field
We show that the mode corresponding to the point of essential spectrum of the
electromagnetic scattering operator is a vector-valued distribution
representing the square root of the three-dimensional Dirac's delta function.
An explicit expression for this singular mode in terms of the Weyl sequence is
provided and analyzed. An essential resonance thus leads to a perfect
localization (confinement) of the electromagnetic field, which in practice,
however, may result in complete absorption.Comment: 14 pages, no figure
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