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 $n$ that admit an $N$-shock type solution with $N\leq n+1$. 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 $t$, 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