Lieb-Robinson bounds for classical anharmonic lattice systems

TL;DR

This paper establishes Lieb-Robinson bounds for classical lattice oscillator systems, including harmonic and certain anharmonic cases, demonstrating locality properties that are volume- and initial-condition independent.

Contribution

It extends Lieb-Robinson bounds to classical anharmonic lattice systems with long-range interactions, covering a specific class of observables.

Findings

Lieb-Robinson bounds proven for harmonic systems

Bounds applicable to certain anharmonic perturbations

Results are volume- and initial-condition independent

Abstract

We prove locality estimates, in the form of Lieb-Robinson bounds, for classical oscillator systems defined on a lattice. Our results hold for the harmonic system and a variety of anharmonic perturbations with long range interactions. The anharmonic estimates are applicable to a special class of observables, the Weyl functions, and the bounds which follow are not only independent of the volume but also the initial condition.