相关论文: Application of the diffraction trace formula to th…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
Scattering by (a) a single composite scatterer consisting of a concentric arrangement of an outer N-slit rigid cylinder and an inner cylinder which is either rigid or in the form of a thin elastic shell and (b) by a finite periodic array of…
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…
We provide an analytical formulation to model the propagation of elastic waves in a homogeneous half-space supporting an array of thin plates. The technique provides the displacement field obtained from the interaction between an incident…
This work applies Mie scattering theory to provide a new perspective on the propagation of light through a spherical obstacle, offering a novel explanation for the formation of the Poisson spot (also known as the Arago or Fresnel spot). We…
We derive a Gutzwiller-type trace formula for quantum chaotic systems that accounts for both particle spin precession and discrete geometrical symmetries. This formula generalises previous results that were obtained either for systems with…
This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace…
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
The diffraction patterns of crystalline materials with local order contain sharp Bragg reflections as well as highly structured diffuse scattering. The instrumental requirements, experimental parameters and data processing techniques for…
We study the properties of the two-point spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a…
We derive a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences and discontinuities occurring at bifurcation points and in the spherical limit, the trace integrals over…
We determine semiclassical quasienergy spectra from periodic orbits for a system with a mixed phase space, the kicked top. Throughout the transition from integrability to well developed chaos the standard error incurred for the…
Different theoretical methods used for the description of diffractive processes in small-x deep inelastic scattering are reviewed. The semiclassical approach, where a partonic fluctuation of the incoming virtual photon scatters off a…
The scattering of fast charged particles in a bent crystal has been analyzed in the framework of relativistic classical mechanics. The expressions obtained for the deflection function are in satisfactory agreement with the experimental data…
In this work, we discuss the way in which electric and magnetic dipole resonances arising in the optical scattering spectrum of non-absorbing dielectric nanospheres can be accurately approximated by means of simple explicit expressions that…
As a contribution to the inverse scattering problem for classical chaotic systems, we show that one can select sequences of intervals of continuity, each of which yields the information about period, eigenvalue and symmetry of one unstable…
Recent observations of rapidly rotating stars have revealed the presence of regular patterns in their pulsation spectra. This has raised the question as to their physical origin, and in particular, whether they can be explained by an…
In this paper, the regularized trace formulas for a diffusion operator which include conformable fractional derivatives of order {\alpha} (0<{\alpha \leq 1}) is obtained.