Alberto Maiocchi

Exponentially Long Stability Times for a Nonlinear Lattice in the Thermodynamic Limit

In this paper, we construct an adiabatic invariant for a large 1–d lattice of particles, which is the so called Klein Gordon lattice. The time evolution of such a quantity is bounded by a stretched exponential as the perturbation parameters tend to zero. At variance with the results available in the literature, our result holds uniformly in the thermodynamic limit. The proof consists of two steps: first, one uses techniques of Hamiltonian perturbation theory to construct a formal adiabatic invariant; second, one uses probabilistic methods to show that, with large probability, the adiabatic invariant is approximately constant. As a corollary, we can give a bound from below to the relaxation time for the considered system, through estimates on the autocorrelation of the adiabatic invariant.

An averaging theorem for FPU in the thermodynamic limit

Consider an FPU chain composed of

Relaxation Times for Hamiltonian Systems

N\gg 1

Chaoticity threshold in magnetized plasmas: numerical results in the weak coupling regime.

N≫1 particles, and endow the phase space with the Gibbs measure corresponding to a small temperature

The effective equation method

\beta ^{-1}

Persistence of regular motions for nearly integrable Hamiltonian systems in the thermodynamic limit

β-1. Given a fixed