Asymptotic boundary layer method for unstable trajectories : Semiclassical expansions for individual scar wavefunctions.

We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field

Dynamic inverse problem in a weakly laterally inhomogeneous medium

An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an interface. An assumption of a weak lateral inhomogeneity means that the velocity of wave propagation and the shape of the interface depend weakly on the horizontal coordinates, $x=(x_1,x_2)$, in comparison with the strong dependence on the vertical coordinate, $z$, giving rise to a small parameter \e <<1. Expanding the velocity in power series with respect to \e, we obtain a recurrent system of 1D inverse problems. We provide algorithms to solve these problems for the zero and first-order approximations. In the zero-order approximation, the corresponding 1D inverse problem is reduced to a system of non-linear Volterra-type integral equations. In the first-order approximation, the corresponding 1D inverse problem is reduced to a system of coupled linear Volterra integral equations. These equations are used for the numerical reconstruction of the velocity in both layers and the interface up to O(\e^2).Comment: 12 figure

Reconstruction of the reflection coefficient and interface in homogeneous medium by means of Gaussian jets

This paper is devoted to the inverse problem of reconstruction of a shape of interface separating two homogeneous media in acoustic approximation from from the knowledge of the scattered field data. It is assumed that the infinitely smooth surface representing the interface is illuminated by an incident Gaussian jet described as a high-frequency non-stationary localized asymptotic solution (wave package). The parameters of the medium above the interface are known. Measuring the intensity of the reflected Gaussian jet along a horizontal line placed at some height above the interface gives the inverse data to solve the problem of reconstruction of a shape of interface as well as determination of velocity of wave propagation and density below the interface. In the paper we describe a corresponding algorithm of solving the inverse problem and demonstrate a few examples of its numerical testing

Electromagnetic guided waves on linear arrays of spheres

Guided electromagnetic waves propagating along one-dimensional arrays of dielectric spheres are studied. The quasi-periodic wave field is constructed as a superposition of vector spherical wavefunctions and then application of the boundary condition on the sphere surfaces leads to an infinite system of real linear algebraic equations. The vanishing of the determinant of the associated infinite matrix provides the condition for surface waves to exist and these are determined numerically after truncation of the infinite system. Dispersion curves are presented for a range of azimuthal modes and the effects of varying the sphere radius and electric permittivity are shown. We also demonstrate that a suitable truncation of the full system is precisely equivalent to the dipole approximation that has been used previously by other authors, in which the incident field on a sphere is approximated by its value at the centre of that sphere. © 2012 Elsevier B.V

Inverse problem of velocity reconstruction in weakly lateral heterogeneous half-space

A wave propagation generated by a boundary source into a weakly lateral heterogeneous medium (WLHM) occupying a half-space is considered in the acoustic approximation. WLHM means that the velocity of the wave propagation depends weakly on the horizontal coordinates in comparison with the strong dependence on the vertical coordinate z. We consider the problem of the reconstruction of the velocity inside the half-space from the knowledge of the medium response measured at z=0. We obtain a recurrent system of 1D inverse problems to find..

Localised States of Fabry-Perot Type in Graphene Nano-Ribbons

This book collects some new progresses on research of graphene from theoretical and experimental aspects in a variety of topics, such as graphene nanoribbons, graphene quantum dots, and graphene-based resistive switching memory. The authors of each chapter give a unique insight about the specific intense research area of graphene. This book is suitable for graduate students and researchers with background in physics, chemistry, and materials as reference

Regular Oscillation Sub-spectrum of Rapidly Rotating Stars

We present an asymptotic theory that describes regular frequency spacings of pressure modes in rapidly rotating stars. We use an asymptotic method based on an approximate solution of the pressure wave equation constructed from a stable periodic solution of the ray limit. The approximate solution has a Gaussian envelope around the stable ray, and its quantization yields the frequency spectrum. We construct semi-analytical formulas for regular frequency spacings and mode spatial distributions of a subclass of pressure modes in rapidly rotating stars. The results of these formulas are in good agreement with numerical data for oscillations in polytropic stellar models. The regular frequency spacings depend explicitly on internal properties of the star, and their computation for different rotation rates gives new insights on the evolution of mode frequencies with rotation.Comment: 14 pages, 10 figure