Related papers: Phase Space Evolution and Discontinuous Schr\"odin…
In this paper, we consider the Schr\"odinger equation in one space-dimension with potential and we aim at exhibiting dynamic interaction phenomena produced by the potential. To this end, we focus our attention on the time-asymptotic…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
Propagation, transmission and reflection properties of linearly polarized plane waves and arbitrarily short electromagnetic pulses in one-dimensional dispersionless dielectric media possessing an arbitrary space-time dependence of the…
We consider asymmetric (nonreciprocal) wave transmission through a layered nonlinear, non mirror-symmetric system described by the one-dimensional Discrete Nonlinear Schr\"odinger equation with spatially varying coefficients embedded in an…
For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schr\"odinger equation consists of several equations, one for each time variable. This…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
We study a generalization of Husimi function in the context of wavelets. This leads to a nonnegative density on phase-space for which we compute the evolution equation corresponding to a Schr\"Aodinger equation.
This study unveils the time-space transforms underlying anomalous diffusion process. Based on this finding, we present the two hypotheses concerning the effect of fractal time-space fabric on physical behaviors and accordingly derive…
The diffraction of electromagnetic waves by screens (apertures in screens) with time-varying dimensions is studied. The generalized vector Kirchhoff's representation for this case is obtained. It is also shown that with accuracy up to the…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
A nonlinear Schr\"odinger equation for the envelope of two dimensional surface water waves on finite depth with non zero constant vorticity is derived, and the influence of this constant vorticity on the well known stability properties of…
We present spatio-temporal characteristics of spreading depolarizations (SD) in two experimental systems: retracting SD wave segments observed with intrinsic optical signals in chicken retina, and spontaneously occurring re-entrant SD waves…
Light propagation through turbulence produces speckles, whose ensemble behavior is typically characterized by snapshot intensity statistics. Here, we track the spatiotemporal evolution of individual speckles and quantify fragmentation,…
In this article, we study wave dynamics in the fractional nonlinear Schr\"odinger equation with a modulated honeycomb potential. This problem arises from recent research interests in the interplay between topological materials and nonlocal…
The stationary eigenstates and eigenvalues for the ponderomotive potential of an optical crystal confined in a one-dimensional infinite square well are numerically obtained. The initial states of the incoming particles taken as Gaussian,…
We consider the cubic nonlinear Schrodinger equation with a potential in one space dimension. Under the assumptions that the potential is generic, sufficiently localized, and does not have bound states, we obtain the long time asymptotic…
An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…
Under the impact of an infinitely extended edge phase dislocation, optical vortices (screw phase dislocations) induce scintillation enhancement. The scintillation index of a beam consisting of two Gaussian vortex beams with ${\pm{1}}$…
We present numerical simulations of coupled Ginzburg-Landau equations describing parametrically excited waves which reveal persistent dynamics due to the occurrence of phase slips in sequential pairs, with the second phase slip quickly…
Localized scattering phenomena may result in the formation of stationary matter waves originating from a compact region in physical space. Mathematically, such waves are advantageously expressed in terms of quantum sources that are…