# Dynamics of Infinite Classical Anharmonic Crystals

@article{Butt2016DynamicsOI, title={Dynamics of Infinite Classical Anharmonic Crystals}, author={Paolo Butt{\`a} and Carlo Marchioro}, journal={Journal of Statistical Physics}, year={2016}, volume={164}, pages={680-692} }

We consider an unbounded lattice and at each point of this lattice an anharmonic oscillator, that interacts with its first neighborhoods via a pair potential V and is subjected to a restoring force of potential U. We assume that U and V are even nonnegative polynomials of degree $$2\sigma _1$$2σ1 and $$2\sigma _2$$2σ2. We study the time evolution of this system, with a control of the growth in time of the local energy, and we give a nontrivial bound on the velocity of propagation of a…

## One Citation

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This work considers discrete analogues of two well-known open problems regarding invariant measures for dispersive PDE, namely, the invariance of the Gibbs measure for the continuum (classical) Heisenberg measure and the consistency of the Higgs measure.

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