Related papers: The evolution of free wave packets
We investigate a class of cosmological solutions of Einstein's field equations in higher dimensions with a cosmological constant and an ideal fluid matter distribution as a source. We discuss the dynamical evolution of the universe subject…
We study the evolution of turbulent puffs by means of high-resolution numerical simulations. Puffs are bunches of passive particles released from an initially spherical distribution at regular time intervals of the order of the Kolmogorov…
We introduce novel sets of measures with the goal of describing dynamical properties of force networks in dense particulate systems. The presented approach is based on persistent homology and allows for extracting precise, quantitative…
We present the first experimental observation of accelerating beams in curved space. More specifically, we demonstrate, experimentally and theoretically, shape-preserving accelerating beams propagating on spherical surfaces: closed-form…
We propose a general construction of wave functions of arbitrary prescribed fractal dimension, for a wide class of quantum problems, including the infinite potential well, harmonic oscillator, linear potential and free particle. The…
We consider an electron wave packet evolution in the external deterministic electric field with Gaussian white noise addition. An explicit expression was given for the averaged probability flux with Gaussian initial wave function. We show…
It is demonstrated that -- contrary to the common belief -- it is possible to construct solutions of the non-relativistic Schr\"odinger equation of a free particle, that do not exhibit dispersion. However, it seems that no normalizable wave…
The problem of a viscous flow past a submerged source starting from rest and moving with a constant velocity, below and parallel to a free surface is examined. Asymptotic expressions for long-time evolution of free-surface elevation are…
The time evolution of initially localized wavepackets in the discrete Hatano-Nelson lattice displays a rich dynamical structure shaped by the interplay between dispersion and nonreciprocity. Our analysis reveals a characteristic evolution…
A new method for investigating relaxation phenomena for charge carriers hopping between localized tail states has been developed. It allows us to consider both charge and energy {\it dispersive} transport. The method is based on the idea of…
We present here the transmission of electromagnetic waves through layered structures of metallic and left-handed media. Based on the theory of finite periodic systems, we show that besides the strong influence of the incidence angle, the…
We study the spreading of single-site excitations in one-dimensional disordered Klein-Gordon chains with tunable nonlinearity $|u_{l}|^{\sigma} u_{l}$ for different values of $\sigma$. We perform extensive numerical simulations where wave…
Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's…
We introduce a model of information packet transport on networks in which the packets are posted by a given rate and move in parallel according to a local search algorithm. By performing a number of simulations we investigate the major…
We study the evolution of graphs densifying by adding edges: Two vertices are chosen randomly, and an edge is (i) established if each vertex belongs to a tree; (ii) established with probability $p$ if only one vertex belongs to a tree;…
The time evolution of wave packets in a harmonic oscillator potential is studied. Some new results for the most general case are obtained. A natural number, called ``degree of rigidity'', is introduced to describe qualitatively how much the…
Non-Hermitian (NH) systems have attracted great attention due to their exotic phenomena beyond Hermitian domains. Here we study the wave-packet dynamics in general one-dimensional NH lattices and uncover several unexpected phenomena. The…
We study the space-time evolution of ``flavor'' neutrino wave-packets at finite temperature and density in the early Universe prior to BBN. We implement non-equilibrium field theory methods and linear response to study the space-time…
We analyse the evolution of cosmological perturbations which leads to the formation of large voids in the distribution of galaxies. We assume that perturbations are spherical and all components of the Universe - radiation, matter and dark…
We construct wave packets for the hydrogen atom labelled by the classical action-angle variables with the following properties. i) The time evolution is exactly given by classical evolution of the angle variables. (The angle variable…