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


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2012-08

AUTHORS

Andrea Carati, Alberto Mario Maiocchi

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. More... »

PAGES

129-161

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00220-012-1522-z

DOI

http://dx.doi.org/10.1007/s00220-012-1522-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1040875907


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