The Kramers equation simulation algorithm I. Operator analysis

TL;DR

This paper introduces an operator-based framework for simulating the Kramers equation, developing algorithms that can be precisely tuned for accuracy and efficiency, including methods to reduce autocorrelations and restore detailed balance.

Contribution

It presents a novel operatorial formalism for the Kramers equation, enabling the design of high-order, adjustable algorithms with improved sampling properties.

Findings

Algorithms can be made precise at any order in time step

Free parameters help reduce autocorrelations

Global Metropolis test restores detailed balance

Abstract

Using an operatorial formalism, we study the Kramers equation and its applications to numerical simulations. We obtain classes of algorithms which may be made precise at every desired order in the time step $\epsilon$ and with a set of free parameters which can be used to reduce autocorrelations. We show that it is possible to use a global Metropolis test to restore Detailed Balance.