Related papers: Wath Time an Incident Wave Packet is Reflected?
Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination of their group velocity with respect to the vertical is completely determined by their frequency. Therefore…
We consider the problem of shock reflection on a solid wall in plane symmetry for a barotropic fluid. We establish a local in time solution after the point of reflection, thereby determining the state behind the reflected shock. The…
We show that the delay time distribution for wave reflection from a one-dimensional random potential is related directly to that of the reflection coefficient, derived with an arbitrarily small but uniform imaginary part added to the random…
We consider the one-dimensional Schr\"odinger equation with a potential satisfying the standard assumptions of the inverse scattering theory and supported on the half-line $x\ge 0$. For this equation at fixed positive energy we give…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
The inverse scattering problem for the Schr$\mathrm{\ddot{o}}$dinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely…
We study numerically the dynamics of a one-electron wave packet in a two-dimensional random lattice with long-range correlated diagonal disorder in the presence of a uniform electric field. The time-dependent Schr\"{o}dinger equation is…
The refraction of space-time (ST) wave packets offers many fascinating surprises with respect to conventional pulsed beams. In paper (I) of this sequence, we described theoretically the refraction of all families of ST wave packets at…
In this paper, scattering of incident plane waves from rough surfaces have been modeled in a fractional space. It is shown how wave scattering from a rough surface, could be a simple reflection problem in a fractional space. In the integer…
We consider the superposition of plane waves and localized wave packets. This kind of wave function can result from a local excitation of a particle described by a plane wave. For charged particles, the wave packet means a current, the time…
We study the time required for a wave packet to tunnel beyond a square barrier, or to be reflected, by envisaging a physical clock which ticks only when the particle is within the barrier region. The clock consists in a magnetic moment…
The problem of Schr\"odinger propagation of a discontinuous wavefunction -diffraction in time- is studied under a new light. It is shown that the evolution map in phase space induces a set of affine transformations on discontinuous…
We present an exact solution to the one-dimensional (1-D) scattering-from-a-barrier problem for an incident neutron described by a wave packet. As an aid to presenting our approach, we spend some time on a basic review of how wave packets…
Wave packet revivals and fractional revivals are striking quantum interference phenomena that can occur under suitable conditions in a system with a nonlinear spectrum. In the framework of a specific model (the propagation of an initially…
A curious effect is uncovered by calculating the it time evolving probability of reflection of a Gaussian wave packet from a rectangular potential barrier while it is perturbed by reducing its height. A time interval is found during which…
The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schr\"odinger equation. The fact that the potential term…
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…
Time reflection and refraction are temporal analogies of the spatial boundary effects derived from Fermat's principle. They occur when classical waves strike a time boundary where an abrupt change in the properties of the medium is…
A detailed theoretical investigation of the reflection of an atomic de Broglie wave at an evanescent wave mirror is presented. The classical and the semiclassical descriptions of the reflection process are reviewed, and a full…
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…