153,762 research outputs found
Space-time resonances
This article is a short exposition of the space-time resonances method. It
was introduced by Masmoudi, Shatah, and the author, in order to understand
global existence for nonlinear dispersive equations, set in the whole space,
and with small data. The idea is to combine the classical concept of
resonances, with the feature of dispersive equations: wave packets propagate at
a group velocity which depends on their frequency localization. The analytical
method which follows from this idea turns out to be a very general tool.Comment: 10 page
Exponential decay and resonances in a driven system
We study the resonance phenomena for time periodic perturbations of a
Hamiltonian on the Hilbert space . Here, resonances are
characterized in terms of time behavior of the survival probability. Our
approach uses the Floquet-Howland formalism combined with the results of L.
Cattaneo, J.M. Graf and W. Hunziker on resonances for time independent
perturbations.Comment: 16 page
Frobenius-Perron Resonances for Maps with a Mixed Phase Space
Resonances of the time evolution (Frobenius-Perron) operator P for phase
space densities have recently been shown to play a key role for the
interrelations of classical, semiclassical and quantum dynamics. Efficient
methods to determine resonances are thus in demand, in particular for
Hamiltonian systems displaying a mix of chaotic and regular behavior. We
present a powerful method based on truncating P to a finite matrix which not
only allows to identify resonances but also the associated phase space
structures. It is demonstrated to work well for a prototypical dynamical
system.Comment: 5 pages, 2 figures, 2nd version as published (minor changes
Dynamics of a Classical Particle in a Quasi Periodic Potential
We study the dynamics of a one-dimensional classical particle in a space and
time dependent potential with randomly chosen parameters. The focus of this
work is a quasi-periodic potential, which only includes a finite number of
Fourier components. The momentum is calculated analytically for short time
within a self-consistent approximation, under certain conditions.
We find that the dynamics can be described by a model of a random walk
between the Chirikov resonances, which are resonances between the particle
momentum and the Fourier components of the potential. We use numerical methods
to test these results and to evaluate the important properties, such as the
characteristic hopping time between the resonances. This work sheds light on
the short time dynamics induced by potentials which are relevant for optics and
atom optics
Quantum corrections for pion correlations involving resonance decays
A method is presented to include quantum corrections into the calculation of
two-pion correlations for the case where particles originate from resonance
decays. The technique uses classical information regarding the space-time
points at which resonances are created. By evaluating a simple thermal model,
the method is compared to semiclassical techniques that assume exponential
decaying resonances moving along classical trajectories. Significant
improvements are noted when the resonance widths are broad as compared to the
temperature.Comment: 9 pages, 4 figure
Classical versus Quantum Time Evolution of Densities at Limited Phase-Space Resolution
We study the interrelations between the classical (Frobenius-Perron) and the
quantum (Husimi) propagator for phase-space (quasi-)probability densities in a
Hamiltonian system displaying a mix of regular and chaotic behavior. We focus
on common resonances of these operators which we determine by blurring
phase-space resolution. We demonstrate that classical and quantum time
evolution look alike if observed with a resolution much coarser than a Planck
cell and explain how this similarity arises for the propagators as well as
their spectra. The indistinguishability of blurred quantum and classical
evolution implies that classical resonances can conveniently be determined from
quantum mechanics and in turn become effective for decay rates of quantum
correlations.Comment: 10 pages, 3 figure
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