Related papers: Evolution of piecewise polynomial wave functions
We develop a formalism for treating coherent wave-packet dynamics of charge and spin carriers in degenerate and nearly degenerate bands. We consider the two-band case carefully in view of spintronics applications, where transitions between…
On the viewpoint of corpuscular model an electromagnetic radiation can be regarded as a system composed of photons with different energies and momenta, which provides us a method being different from the Maxwell wave theory to describe the…
Multivariate piecewise polynomial functions (or splines) on polyhedral complexes have been extensively studied over the past decades and find applications in diverse areas of applied mathematics including numerical analysis, approximation…
Because surface plasmon polaritons (SPPs) are surface waves characterized by one free transverse dimension, the only monochromatic diffraction-free spatial profiles for SPPs are cosine and Airy waves. Pulsed SPP wave packets have been…
An exploratory study of two-particle wave function is carried out with a four dimensional simple model. The wave functions not only for two-particle ground and first excited states but also for an unstable state are calculated from three-…
We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the…
The evolution of random wave fields on the free surface is a complex process which is not completely understood nowadays. For the sake of simplicity in this study we will restrict our attention to the 2D physical problems only (i.e. 1D wave…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
Over the years, the directional distribution functions of wind-generated wave field have been assumed to be unimodal. While details of various functional forms differ, these directional models suggest that waves of all spectral components…
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the…
In the first paper in this series, we introduced "persistent gravitational wave observables" as a framework for generalizing the gravitational wave memory effect. These observables are nonlocal in time and nonzero in the presence of…
The spatial Dysthe equations describe the envelope evolution of the free-surface and potential of gravity waves in deep waters. Their Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new…
To better understanding the principal features of collisionless damping/growing plasma waves we have implemented a demonstrative calculation for the simplest cases of electron waves in two-stream plasmas with the delta-function type…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
The spatial version of the fourth-order Dysthe equations describe the evolution of weakly nonlinear narrowband wave trains in deep waters. For unidirectional waves, the hidden Hamiltonian structure and new invariants are unveiled by means…
We derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier multipliers with finitely smooth symbols at the origin.…
We describe the evolution of a paraxial electromagnetic wave characterizing by a non-uniform polarization distribution with singularities and propagating in a weakly anisotropic medium. Our approach is based on the Stokes vector evolution…
Owing to the non-differentiable nature of the theory of Scale Relativity, the emergence of complex wave functions, then of spinors and bi-spinors occurs naturally in its framework. The wave function is here a manifestation of the velocity…
A conditional kinetic energy is defined in terms of the Wigner distribution. It is shown that this kinetic energy may become negative for negative Wigner distributions. A free particle wave packet with negative kinetic energy will spread in…
The evolution of a composite closed system using the integral wave equation with the kernel in the form of path integral is considered. It is supposed that a quantum particle is a subsystem of this system. The evolution of the reduced…