Related papers: Wave packet dynamics and factorization of numbers
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new,…
The numerical prediction, theoretical analysis, and experimental verification of the phenomenon of wave packet revivals in quantum systems has flourished over the last decade and a half. Quantum revivals are characterized by initially…
The revival structure of wave packets is examined for quantum systems having energies that depend on two nondegenerate quantum numbers. For such systems, the evolution of the wave packet is controlled by two classical periods and three…
Wave packet revivals and fractional revivals are striking quantum interference phenomena that can occur under suitable conditions in a system with a nonlinear spectrum. In the framework of a specific model (the propagation of an initially…
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…
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…
Wave packet fractional revivals is a relevant feature in the long time scale evolution of a wide range of physical systems, including atoms, molecules and nonlinear systems. We show that the sum of information entropies in both position and…
The revival structure of Stark wave packets is considered. These wave packets have energies depending on two quantum numbers and are characterized by two sets of classical periods and revival times. The additional time scales result in…
The internal phase dynamics of a quantum system is revealed in details. Theoretical and experimental evidences of existence of a causal relation of the phase of the wave function with the dynamics of the quantum system are presented…
The recurrence phenomena of an initially well localized wave packet are studied in periodically driven power-law potentials. For our general study we divide the potentials in two kinds, namely tightly binding and loosely binding potentials.…
We present theoretical study of revival phenomena for a wave packet initially well localized in a one-dimensional potential in the presence of an external periodic modulating field. The classical motion, revival, and super-revival time…
Talbot effect in the space-time evolution of matter waves is analyzed and shown that the matter waves at relativistic and non-relativistic velocities exhibit coherence beyond the grating and display Talbot self-imaging. The grating is…
The phenomenon of wave packet diffraction in space and time is described. It consists in a diffraction pattern whose spatial location progresses with time. The pattern is produced by wave packet quantum scattering off an attractive or…
We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed,…
We develop a quantum landscape approach to characterize the long-time behavior of wave packet spreading in linear open quantum systems. Instead of treating diffusion, localization, and collapse of the wave packet as separate dynamical…
We propose a simple way to determine the periodicities of wave packets in quantum systems directly from the energy differences of the states involved. The resulting classical periods and revival times are more accurate than those obtained…
We study the time evolution of wave packets at the mobility edge of disordered non-interacting electrons in two and three spatial dimensions. The results of numerical calculations are found to agree with the predictions of scaling theory.…
We study the dynamics of a wavepacket in a potential formed by the sum of a periodic lattice and of a parabolic potential. The dynamics of the wavepacket is essentially a superposition of ``local Bloch oscillations'', whose frequency is…
Wave packets in a system governed by a Hamiltonian with a generic nonlinear spectrum typically exhibit both full and fractional revivals. It is shown that the latter can be eliminated by inducing suitable geometric phases in the states, by…
Localized quantum wave packets can be produced in a variety of physical systems and are the subject of much current research in atomic, molecular, chemical, and condensed-matter physics. They are particularly well suited for studying the…