相关论文: Mean Sinc Sums and Scale Invariant Scattering
The scattering problem can be implemented in a square-integrable basis via the so-called $J$-matrix method. While methods to compute the phase shift in the $J$-matrix approach are known, we introduce a novel formula in square-integrable…
Recently, in Quantum Field theory, there has been an interest in scattering in highly singular potentials. Here, solutions to the stationary Schroedinger equation are presented when the potential is a multiple of an arbitrary positive power…
We theoretically and numerically demonstrate that completely integrable scattering processes may exhibit fractal transmission fluctuations, due to typical spectral properties of integrable systems. Similar properties also occur with…
We study scaling properties of stochastic aggregation processes in one dimension. Numerical simulations for both diffusive and ballistic transport show that the mass distribution is characterized by two independent nontrivial exponents…
The primary objective of the present paper is to develop the theory of quantization dimension of an invariant measure associated with an iterated function system consisting of finite number of contractive infinitesimal similitudes in a…
A simplified Randall-Sundrum-like model in 6 dimensions is discussed. The extra two dimensions correspond to the cone. The effective four-dimensional scalar self-interacting theory is studied at one-loop level. The contributions due to…
Dilatation, i.e. scale, symmetry in the presence of the dilaton in Minkowski space is derived from diffeomorphism symmetry in curved spacetime, incorporating the volume-preserving diffeomorphisms. The conditions for scale invariance are…
The scattering amplitude for the recently discovered exactly solvable shape invariant potential, which is isospectral to the generalized P\"oschl-Taylor potential, is calculated explicitly by considering the asymptotic behavior of the…
A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying $\mathcal{PT}$-symmetry. It is illustrated that unlike in…
The present paper generalizes preceding papers of the author and opens a cycle of works concerning the general posing and solution in analytic form of the quantum-mechanical inverse scattering problem (for a given partial channel) in a…
Wave localization is a ubiquitous phenomenon. It refers to situations that transmitted waves in scattering media are trapped in space and remain confined in the vicinity of the initial site until dissipated. Based on a scaling analysis, the…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
We give a revealing expose that addresses an important issue in scattering theory of how to construct two asymptotically sinusoidal solutions of the wave equation with a phase shift using the same basis having the same boundary conditions…
The role of turbulence in a spherically symmetric accreting system has been studied on very large spatial scales of the system. This is also a highly subsonic flow region and here the accreting fluid has been treated as nearly…
In various subdisciplines of optics and photonics, Mie theory has been serving as a fundamental language and play indispensable roles widely. Conventional studies related to Mie scattering largely focus on local properties such as…
We give a complete solution of the problem of constructing a scattering potential v(x) that possesses scattering properties of one's choice at an arbitrary prescribed wavenumber. Our solution involves expressing v(x) as the sum of at most…
Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be…
We present a general construction of two types of differential forms, based on any $(n{-}3)$-dimensional subspace in the kinematic space of $n$ massless particles. The first type is the so-called projective, scattering forms in kinematic…
It is well known that string theory generates the idea of higher dimensional spacetime instead of the (3+1) dimensions, in which we seem to live. It indicates that the extra space dimensions may remain curled up into very small space. In…
In this paper the scattering between the non-topological kinks arising in a family of two-component scalar field theory models is analyzed. A winding charge is carried by these defects. As a consequence, two different classes of kink…