Extended Variable Methods

Abstract

In the previous chapter we described numerical methods for solving the equations of Langevin dynamics, a system of stochastic differential equations that sample the canonical ensemble. The methods allow us to compute averages of the form (Formula Presented), and H is the system Hamiltonian. In this chapter we extend the range of systems that can be used to accomplish this task using methods based on the incorporation of auxiliary variables. We also consider schemes for sampling alternative thermodynamic ensembles, for example those defined by constant number of atoms N, pressure P and temperature T. In some of the methods, based on purely deterministic models, the ergodic property may be compromised, so an important issue is to design schemes that restore this. We will focus on methods that introduce random processes in direct contact with the auxiliary variables.