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. © 2012 Springer-Verlag.

Carati, A., Maiocchi, A. (2012). Exponentially Long Stability Times for a Nonlinear Lattice in the Thermodynamic Limit. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 314(1), 129-161 [10.1007/s00220-012-1522-z].

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

Maiocchi A. M.
2012

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. © 2012 Springer-Verlag.
Articolo in rivista - Articolo scientifico
Adiabatic invariant; perturbation theory; thermodynamic limit
English
129
161
33
Carati, A., Maiocchi, A. (2012). Exponentially Long Stability Times for a Nonlinear Lattice in the Thermodynamic Limit. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 314(1), 129-161 [10.1007/s00220-012-1522-z].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/349173
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