The ideal energy of classical lattice dynamics

TL;DR

This paper introduces local quantum-mechanical limits on energy and momentum in classical lattice dynamics, showing these limits evolve similarly to classical energy and momentum in specific examples.

Contribution

It defines local quantum limits for energy and momentum in classical lattice systems based on finite-state change rates, linking quantum and classical dynamics.

Findings

Local energy and momentum limits depend on finite-state change rates.

In examples, these limits evolve like classical energy and momentum.

Provides a new perspective on quantum-classical correspondence in lattice dynamics.

Abstract

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.