Related papers: The Gaussian Wave Packet Transform via Quadrature …
Generalization of Gaussian trial wave functions in quantum molecular dynamics models is introduced, which allows for long-range correlations characteristic for composite nuclear fragments. We demonstrate a significant improvement in the…
The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there is another class of unitary transforms,…
We solve the Cauchy problem for the $n$-dimensional wave equation using elementary properties of the Fourier transform.
We simulate the transformation of a classical fluid into a quantum-like (super)-fluid by the application of a generalized quantum potential through a retro-active loop. This numerical experiment is exemplified in the case of a non-spreading…
Generalization of Gaussian trial wave functions in quantum molecular dynamics models is introduced, which allows for long-range correlations characteristic for composite nuclear fragments. We demonstrate a significant improvement in the…
Gaussian wave packets (GWPs) are well suited as basis functions to describe the time evolution of arbitrary wave functions in systems with nonsingular smooth potentials. They are less so in atomic systems on account of the singular behavior…
Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…
An exact closed-form representation is derived of a vector elegant Laguerre-Gaussian wave packet. Its space-time representation consists of three mutually orthogonal field components - of a common azimuthal index and different radial…
We discuss a method by which quantum fluctuations can be included in microscopic transport models based on wave packets that are not energy eigenstates. By including the next-to-leading order term in the cumulant expansion of the…
Interference is one of the most fundamental features which characterizes quantum systems. Here we provide an exhaustive analysis of the interfere dynamics associated with wave-packet superpositions from both the standard quantum-mechanical…
The study of wave packet is of great significance in quantum mechanics, optics and fluid mechanics. However, in order to solve the strict evolution behavior of wave packet, it is necessary not only to determine the parameters of various…
In this article we present an exact and unified description of wave-packet dynamics in various 2D systems in presence of a transverse magnetic field. We consider an initial minimum-uncertainty Gaussian wave-packet, and find that its long…
We propose an implementation of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform occurs naturally in the unitary time evolution of energy eigenstates and is used to define an…
We present a generic treatment of wave-packet revivals for quantum-mechanical systems. This treatment permits a classification of certain ideal revival types. For example, wave packets for a particle in a one-dimensional box are shown to…
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…
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…
Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns…
A theoretical analysis, aimed at characterizing the degradation induced by the resampling and requantization processes applied to band-limited Gaussian signals with flat power spectrum, available through their digitized samples, is…
Conventional method for Gaussian beam collimation is to expand the beam waist to achieve a smaller divergence angle. Recent transformation optics offers an unconventional path to control the electromagnetic field. In this paper we show that…
The properties of quantum mechanics with a discrete phase space are studied. The minimum uncertainty states are found, and these states become the Gaussian wave packets in the continuum limit. With a suitably chosen Hamiltonian that gives…