Title :

On (in)elastic non-dissipative Lorentz gases and the (in)stability of classical pulsed and kicked rotors

Author(s) :

Aguer, Bénédicte [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
De Bievre, Stephan [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
SImulations and Modeling for PArticles and Fluids [SIMPAF]

Journal title :

Journal of Physics A: Mathematical and Theoretical

Pages :

47001

Publisher :

IOP Publishing

Publication date :

2011

ISSN :

1751-8113

HAL domain(s) :

Mathématiques [math]/Physique mathématique [math-ph]

English abstract : [en]

We study numerically and theoretically the d dimensional Hamiltonian motion of fast particles through a field of scatterers, modeled by bounded, localized, (time-dependent) potentials. We illustrate the wide applicability ...
Show more >We study numerically and theoretically the d dimensional Hamiltonian motion of fast particles through a field of scatterers, modeled by bounded, localized, (time-dependent) potentials. We illustrate the wide applicability of a random walk picture previously developed for a field of scatterers with random spatial and/or time-dependence by applying it to four other models. First, for a periodic array of spherical scatterers in d>=2, with a smooth (quasi)periodic time-dependence, we show Fermi acceleration: the ensemble averaged kinetic energy <||p(t)||^2> grows as t^(2/5). Nevertheless, the mean squared displacement <||q(t)||^2> ~ t^2 behaves ballistically. These are the same growth exponents as for random time-dependent scatterers. Second, we show that in the soft elastic and periodic Lorentz gas, where the particles' energy is conserved, the motion is diffusive, as in the standard hard Lorentz gas, but with a diffusion constant that grows as ||p_0||^5, rather than only as ||p_0||. Third, we note the above models can also be viewed as pulsed rotors: the latter are therefore unstable in dimension d>=2. Fourth, we consider kicked rotors, and prove them, for sufficiently strong kicks, to be unstable in all dimensions with <||p(t)||^2> ~ t and <||q(t)||^2> ~ t^3. Finally, we analyze the singular case d=1, where the kinetic energy remains bounded in time for time-dependent non-random potentials whereas it grows at the same rate as above in the random case.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL