Data di Pubblicazione:
2012
Citazione:
Exponentially long stability times for a nonlinear lattice in the thermodynamic limit / A. Carati, A. Maiocchi. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 314:1(2012 Aug), pp. 129-161.
Abstract:
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Hamiltonian system; equilibrium point; oscillators; integrals
Elenco autori:
A. Carati, A. Maiocchi
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