Related papers: The split-operator technique for the study of spin…
In this paper, we construct a modified wave operators for Schrodinger equations with time-dependent long-range potentials by using wave packet transform and give a proof of the existence of the modified wave operators.
A translation operator is introduced to describe the quantum dynamics of a position-dependent mass particle in a null or constant potential. From this operator, we obtain a generalized form of the momentum operator as well as a unique…
An extended Wigner function formalism is introduced for describing the quantum dynamics of particles with internal degrees of freedom in the presence of spatially inhomogeneous fields. The approach is used for quantitative simulations of…
A general theory of nonlinear signal-noise interactions for wavelength division multiplexed fiber-optic coherent transmission systems is presented. This theory is based on the regular perturbation treatment of the nonlinear Schrodinger…
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 consider a simple model of one-dimensional magnetic crystal and examine the propagation of an electromagnetic wave through such a medium. Calculating the dispersion relation ${\bf k}(\omega)$ allows us to illustrate how the spread of the…
We analyze the matter wave transmission above a step potential within the framework of the cubic-nonlinear Schr\"odinger equation. We present a comprehensive analysis of the corresponding stationary problem based on an exact second-order…
We bring the set of linear quantum operations, important for many fundamental studies in photonic systems, to the material domain of collective excitations known as spin waves. Using the ac Stark effect we realize quantum operations on…
We consider the dynamics of relativistic spin-half particles in quantum graphs with transparent branching points. The system is modeled by combining the quantum graph concept with the one of transparent boundary conditions applied to the…
Our investigation focuses on the asymptotic spreading behavior of the Fisher-KPP equation with a mixed local-nonlocal operator in the diffusion (see the work by X. Cabr\'e and J.-M. Roquejoffre, 2013, ref.[8]) to the setting of mixed…
The Gaussian Wave-Packet phase-space representation is used to show that the expansion in powers of $\hbar$ of the quantum Liouville propagator leads, in the zeroth order term, to results close to those obtained in the statistical…
We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are…
We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…
Using a density matrix description in space we study the evolution of wavepackets in a fluctuating space-time background. We assume that space-time fluctuations manifest as classical fluctuations of the metric. From the non-relativistic…
It has been suggested that the nonlinear Schr\"odinger-Newton equation might approximate the coupling of quantum mechanics with gravitation, particularly in the context of the M{\o}ller-Rosenfeld semiclassical theory. Numerical results for…
Ideas and results of the generalized wave operator theory for dynamical and stationary cases are developed further and exact expressions for generalized scattering operators are obtained for wide classes of differential equations. New…
Explicit formulas for the analytic extensions of the scattering matrix and the time delay of a quasi-one-dimensional discrete Schr\"odinger operator with a potential of finite support are derived. This includes a careful analysis of the…
We show that combination of a linearly polarized resonant microwave field and a parallel static electric field may be used to create a non-dispersive electronic wavepacket in Rydberg atoms. The static electric field allows for manipulation…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
We investigate the influence of the temporal variations of various medium parameters on the propagation of Dirac-type waves in materials where the quasiparticles are described by a generalized version of the pseudospin-1/2 Dirac equation.…