Science Abstract
Abstract
The Feynman path integral formulation of quantum statistical mechanics
is reviewed in detail. The evaluation of path integrals by
molecular dynamics methods is discussed, and specific algorithms
for treating the quantum canonical (NVT) and isothermal-isobaric (NPT)
ensembles are developed. These
algorithms employ a variety of novel techniques that address the
problem of ergodic phase space sampling and ensure
rapid convergence of quantum equilibrium properties
compared to more standard Monte Carlo approaches.
Specifically, variable transformations, Nosé-Hoover chain thermostatting,
and multiple time scale integration are combined to produce algorithms
that are almost as efficient as the best Monte Carlo methods.
The molecular dynamics approach is often preferable to Monte Carlo,
in that it can be both vectorized and parallelized more efficiently.
In addition, certain methods, such as the Car-Parrinello ab inito
molecular dynamics or the recently introduced adiabatic centroid molecular
dynamics methods are inextricably tied to a dynamical propagation scheme.
In these lectures, the equations of motion that generate the different quantum
ensembles are presented, tested and used in a variety of applications.