相关论文: New physical wavelet 'Gaussian Wave Packet'
The quantum evolution of the Wigner function for Gaussian wave packets generated by a non-Hermitian Hamiltonian is investigated. In the semiclassical limit $\hbar\to 0$ this yields the non-Hermitian analog of the Ehrenfest theorem for the…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
The velocity of a passive particle in a one-dimensional wave field is shown to converge in law to a Wiener process, in the limit of a dense wave spectrum with independent complex amplitudes, where the random phases distribution is invariant…
A gauge field treatment of a current, oscillating at a fixed frequency, of interacting neutral atoms leads to a set of matter-wave duals to Maxwell's equations for the electromagnetic field. In contrast to electromagnetics, the velocity of…
We have studied dynamical properties and quantum tunneling in asymmetric double-well (DW) systems, by solving Schr\"{o}dinger equation with the use of two kinds of spectral methods for initially squeezed Gaussian wavepackets. Time…
An electromagnetic wave-packet propagating in a linear, homogeneous, and isotropic medium changes shape while its envelope travels with different velocities at different points in spacetime. In general, a wave-packet can be described as a…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the…
The self-action features of wave packets propagating in a two-dimensional system of equidistantly arranged fibers are studied analytically and numerically on the basis of the discrete nonlinear Schr\"odinger equation. Self-consistent…
Bose-Einstein condensates with an attractive 1/r interaction and with dipole-dipole interaction are investigated in the framework of the Gaussian variational ansatz introduced by S. Rau, J. Main, and G. Wunner [Phys. Rev. A, submitted]. We…
The Haar wavelet based quasilinearization technique for solving a general class of singular boundary value problems is proposed. Quasilinearization technique is used to linearize nonlinear singular problem. Second rate of convergence is…
The dynamics of a quantum mechanical particle in a time-independent potential are found to contain many interesting phenomena. These are direct consequences of the (typical) existence of more than one time scale governing the problem. This…
Wavepackets in quantum mechanics spread and the Universe in cosmology expands. We discuss a formalism where the two effects can be unified. The basic assumption is that the Universe is determined by a unitarily evolving wavepacket defined…
In the present paper, details are given on the implementation of a wavelet-based analysis tailored to the processing of acoustical signals. The family of the suitable wavelets (`Reimann wavelets') are obtained in the time domain from a…
A gauge-invariant formulation for the gravitational wave equations is presented. Using this approach, weak, plane wave solutions in a vacuum are derived in various theories. These include general relativity with two modes of polarization…
This work focuses on the interaction of an acoustical quasi-Gaussian beam centered on a rigid immovable sphere, during which at least three physical phenomena arise, namely, the (axial) acoustic scattering, the instantaneous force, and the…
A generalisation of the Shannon complex wavelet is introduced, which is related to raised cosine filters. This approach is used to derive a new family of orthogonal complex wavelets based on the Nyquist criterion for Intersymbolic…
New experimental techniques based on non-linear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates,…
Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…