On inelastic non-dissipative Lorentz gases and the instability of classical pulsed and kicked rotorsReport as inadecuate

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1 LPP - Laboratoire Paul Painlevé 2 SIMPAF - SImulations and Modeling for PArticles and Fluids Inria Lille - Nord Europe, LPP - Laboratoire Paul Painlevé

Abstract : 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 quasiperiodic time-dependence, we show Fermi acceleration: the ensemble averaged kinetic energy grows as t^2-5. Nevertheless, the mean squared displacement ~ 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 ~ t and ~ 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.

Author: Bénédicte Aguer - Stephan De Bievre -

Source: https://hal.archives-ouvertes.fr/


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