Generalisation of theory and algorithms for the configurational temperature Nosé–Hoover thermostat.

Abstract

In this dissertation we reformulate the configurational temperature Nos`e-Hoover thermostat proposed by Braga and Travis (C. Braga and K.P. Travis, 2005), using the antisymmetric matrix formalism found in (A. Sergi, 2003). By exploiting the properties of this formalism, and utilising the concept behind the Nos`e-Hoover chain thermostat, we extend our reformulated thermostat to obtain a hybrid configurational-kinetic chain thermostat. This is done with a view to achieving an ergodic sampling of phase space. We derive an integration algorithm, based upon the symmetric Trotter factorisation of the Liouville operator, as well as symplectic position and velocity Verlet integrations schemes, for purposes of comparison. In the case of systems possessing non-harmonic and non-linear interaction potentials, a position-dependent harmonic approximation scheme is presented. The thermostats and integration schemes were tested on one-dimensional harmonic and quartic oscillators, where it was found that the hybrid configurational-kinetic temperature Nos`e-Hoover chain thermostat overcame the ergodicity problem, and the integration scheme based on the Trotter factorisation was the best performing.