Remarks on random evolutions in Hamiltonian representation

TL;DR

This paper demonstrates how telegrapher's equations and certain Poisson-type random walks can be incorporated into the Hamiltonian formalism through a suitable time-dependent rescaling of variables.

Contribution

It introduces a method to embed telegrapher's equations and Poisson-type random walks into the Hamiltonian framework via variable rescaling.

Findings

Telegrapher's equations fit into Hamiltonian formalism.

Poisson-type random walks can be represented Hamiltonianly.

Rescaling of variables is key to this integration.

Abstract

telegrapher's equations and some random walks of Poisson type are shown to fit into the framework of the Hamiltonian formalism after an appropriate time-dependent rescaling of the basic variables has been made.