Related papers: Fractional revivals through R\'enyi uncertainty re…
Wave packet revivals and fractional revivals are studied by means of newly derived uncertainty relations that involve R\'enyi entropies and position and momentum dispersions.
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…
An uncertainty relation for the R\'enyi entropies of conjugate quantum observables is used to obtain a strong Heisenberg limit of the form ${\rm RMSE} \geq f(\alpha)/(\langle N\rangle+\frac12)$, bounding the root mean square error of any…
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…
We study the dynamics of superposed wave packets in a specific nonlinear Hamiltonian which models the wave packet propagation in Kerr-like media and the dynamics of Bose-Einstein condensates. We show the dependence of initial wave packet…
We show that the time frequency analysis of the autocorrelation function is, in many ways, a more appropriate tool to resolve fractional revivals of a wave packet than the usual time domain analysis. This advantage is crucial in…
Since their introduction in the early sixties, the R\'enyi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between…
Wave packet revivals and fractional revivals are hallmark quantum interference phenomena that arise in systems with nonlinear energy spectra, and their signatures in expectation values of observables have been studied extensively in earlier…
Uncertainty relations provide constraints on how well the outcomes of incompatible measurements can be predicted, and, as well as being fundamental to our understanding of quantum theory, they have practical applications such as for…
The $D$-dimensional harmonic system (i.e., a particle moving under the action of a quadratic potential) is, together with the hydrogenic system, the main prototype of the physics of multidimensional quantum systems. In this work we…
Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the…
We investigate quantum R\'enyi entropic quantities, specifically those derived from 'sandwiched' divergence. This divergence is one of several proposed R\'enyi generalisations of the quantum relative entropy. We may define R\'enyi…
We consider a model Hamiltonian describing the interaction of a single-mode radiation field with the atoms of a nonlinear medium, and study the dynamics of entanglement for specific non-entangled initial states of interest: namely, those in…
It is known that the variance and entropy of quantum observables decompose into intrinsically quantum and classical contributions. Here a general method of constructing quantum-classical decompositions of resources such as uncertainty is…
The entropic moments of the probability density of a quantum system in position and momentum spaces describe not only some fundamental and/or experimentally accessible quantities of the system, but also the entropic uncertainty measures of…
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…
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…
Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the…
Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is…
We report fractional revival phenomena in an ultracold matter wave inside a ring waveguide. The specific fractional revival times are precisely identified and corresponding spatial density patterns are depicted. Thorough analyses of the…