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

摘要: We study numerically and theoretically the $d$-dimensional Hamiltonian motion of fast particles through a field scatterers, modeled by bounded, localized, (time-dependent) potentials, that we refer to as (in)elastic non-dissipative Lorentz gases. illustrate wide applicability random walk picture previously developed for scatterers with spatial and/or time-dependence applying it four other models. First, periodic array spherical in $d\geq2$, smooth (quasi)periodic time-dependence, show Fermi acceleration: ensemble averaged kinetic energy $\left $ grows $t^{2/5}$. Nevertheless, mean squared displacement \sim t^2$ behaves ballistically. These are same growth exponents time-dependent scatterers. Second, soft elastic gas, where particles' is conserved, diffusive, standard hard but diffusion constant $\|p_0\|^{5}$, rather than only $\|p_0\|$. Third, note above models can also be viewed pulsed rotors: latter therefore unstable dimension $d\geq 2$. Fourth, consider kicked rotors, prove them, sufficiently strong kicks, all dimensions t$ t^3$. Finally, analyze singular case $d=1$, remains bounded time non-random potentials whereas at rate case.