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We study the time-dependent scattering of a quantum mechanical wave packet at a barrier for energies larger than the barrier height, in the semi-classical regime. More precisely, we are interested in the leading order of the exponentially…
We investigate potential scattering and tunneling dynamics of a particle wavepacket evolving according to the relativistic Schr\"odinger equation (also known as the Salpeter equation). The tunneling properties of the Salpeter equation…
This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…
We study the paraxial wave equation with a randomly perturbed index of refraction, which can model the propagation of a wave beam in a turbulent medium. The random perturbation is a stationary and isotropic process with a general form of…
Scattering of electromagnetic (EM) waves by many small particles (bodies) embedded in a homogeneous medium is studied. Physical properties of the particles are described by their boundary impedances. The limiting equation is obtained for…
We develop a new variant of the wave-packet analysis and solve the tunneling time problem for one particle. Our approach suggests an individual asymptotic description of the quantum subensembles of transmitted and reflected particles both…
The split-operator technique for wave packet propagation in quantum systems is expanded here to the case of propagating wave functions describing Schr\"odinger particles, namely, charge carriers in semiconductor nanostructures within the…
This paper is concerned with the problem of scattering of time-harmonic acoustic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation…
Wave propagation in complex media is a universal problem spanning optics, acoustics, mechanics, and condensed matter physics. While disorder usually causes strong scattering, recent theory predicts that a special class of correlated…
For hole systems with an effective spin 3/2 we analyzed analytically and numerically the evolution of wave packets with the different initial polarizations. The dynamics of such systems is determined by the $4\times 4$ Luttinger…
A long-standing vision of backscatter communications is to provide long-range connectivity and high-speed transmissions for batteryless Internet-of-Things (IoT). Recent years have seen major innovations in designing backscatters toward this…
A theory of electromagnetic (EM) wave scattering by many small particles of an arbitrary shape is developed. The particles are perfectly conducting or impedance. For a small impedance particle of an arbitrary shape an explicit analytical…
We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations,…
We examine the scattering of Ostrovsky wave packets, generated from an incident solitary wave, in a two layered waveguide with a delamination in the centre and soft (imperfect) bonding either side of the centre. The layers of the waveguide…
We use the Dirac continuum model to study the propagation of electronic wave packets in graphene with periodically arranged circular potential steps. The time propagation of the wave packets are calculated using the split-operator method…
We consider a model of electrons in a finite topological insulator. We numerically study the propagation of electronic wave-packets localized near edges of the structure in the presence of defects and random disorder. We compare the…
We compute the time evolving probability of a Gaussian wave packet to be reflected from a rectangular potential barrier which is perturbed by reducing its height. A time interval is found during which this probability of reflection is…
Simple intersections between one-dimensional channels can act as coherent beam splitters for non-interacting electrons. Here we examine how coherent splitting at such intersections is affected by inter-particle interactions, in the special…
We study wave scattering by a finite transversal strip in a discrete square-lattice waveguide with Dirichlet boundary conditions imposed on the strip and the waveguide walls. The setting is motivated as a discrete analogue of the classical…
We analyze wavepacket propagation in traveling wave tubes (TWTs) analytically and numerically. TWT design in essence comprises a pencil-like electron beam in vacuum interacting with an electromagnetic wave guided by a slow-wave structure…