12 research outputs found
Coherent acceleration of material wavepackets in modulated optical fields
We study the quantum dynamics of a material wavepacket bouncing off a
modulated atomic mirror in the presence of a gravitational field. We find the
occurrence of coherent accelerated dynamics for atoms beyond the familiar
regime of dynamical localization. The acceleration takes place for certain
initial phase space data and within specific windows of modulation strengths.
The realization of the proposed acceleration scheme is within the range of
present day experimental possibilities
Integrability and strong normal forms for non-autonomous systems in a neighbourhood of an equilibrium
The paper deals with the problem of existence of a convergent "strong" normal
form in the neighbourhood of an equilibrium, for a finite dimensional system of
differential equations with analytic and time-dependent non-linear term. The
problem can be solved either under some non-resonance hypotheses on the
spectrum of the linear part or if the non-linear term is assumed to be (slowly)
decaying in time. This paper "completes" a pioneering work of Pustil'nikov in
which, despite under weaker non-resonance hypotheses, the nonlinearity is
required to be asymptotically autonomous. The result is obtained as a
consequence of the existence of a strong normal form for a suitable class of
real-analytic Hamiltonians with non-autonomous perturbations.Comment: 10 page
Dynamics of some piecewise smooth Fermi-Ulam Models
We find a normal form which describes the high energy dynamics of a class of
piecewise smooth Fermi-Ulam ping pong models; depending on the value of a
single real parameter, the dynamics can be either hyperbolic or elliptic. In
the first case we prove that the set of orbits undergoing Fermi acceleration
has zero measure but full Hausdorff dimension. We also show that for almost
every orbit the energy eventually falls below a fixed threshold. In the second
case we prove that, generically, we have stable periodic orbits for arbitrarily
high energies, and that the set of Fermi accelerating orbits may have infinite
measure.Comment: 22 pages, 4 figure