Bulgac-Kusnezov-Nos\'e-Hoover thermostats

TL;DR

This paper develops and compares Bulgac-Kusnezov thermostats with Nosé-Hoover control, providing stable algorithms and analyzing their ergodic properties in phase space for canonical sampling.

Contribution

It formulates Bulgac-Kusnezov thermostats using non-Hamiltonian brackets and introduces two Nosé-Hoover controlled variants with efficient algorithms.

Findings

Both Nosé-Hoover variants sample the canonical distribution correctly.

The simple Bulgac-Kusnezov thermostat appears non-ergodic.

Numerical algorithms are systematically derived and tested.

Abstract

In this paper we formulate Bulgac-Kusnezov constant temperature dynamics in phase space by means of non-Hamiltonian brackets. Two generalized versions of the dynamics are similarly defined: one where the Bulgac-Kusnezov demons are globally controlled by means of a single additional Nos\'e variable, and another where each demon is coupled to an independent Nos\'e-Hoover thermostat. Numerically stable and efficient measure-preserving time-reversible algorithms are derived in a systematic way for each case. The chaotic properties of the different phase space flows are numerically illustrated through the paradigmatic example of the one-dimensional harmonic oscillator. It is found that, while the simple Bulgac-Kusnezov thermostat is apparently not ergodic, both of the Nos\'e-Hoover controlled dynamics sample the canonical distribution correctly.