Effective Liouville Equation for Classical Driven Systems

TL;DR

This paper derives an effective Liouville equation for classical systems under rapid external driving, providing a Hamiltonian-like description of their mean motion.

Contribution

It introduces a new method to obtain effective equations and Liouville dynamics for driven classical systems, extending the theoretical framework.

Findings

Derived effective Hamiltonian-like equations for mean motion.

Formulated the Liouville equation for the distribution of mean variables.

Applicable to a broad class of classical driven systems.

Abstract

A large class of classical dynamical systems with an external rapidly oscillating driving action is considered and the effective Hamiltonian-like equations for the mean motion are obtained. The respective Liouville equation for the distribution function of the mean coordinates and momenta is derived.