PRL Abstract
Abstract
A new method for generating the canonical ensemble via continuous dynamics
is presented. The new method is based on controlling the fluctuations
of an arbitrary number of moments of the multidimensional Gaussian momentum
distribution
function. The equations of motion are non-Hamiltonian, and hence have
a nonvanishing phase space compressibility.
By applying the
statistical mechanical theory of non-Hamiltonian systems recently introduced
by the authors [M.E. Tuckerman, C.J. Mundy and G.J. Martyna,
Europhys. Lett. 45,
149 (1999)], the equations are shown to produce the correct canonical
phase space distribution function. Reversible integrators for the new
equations of motion are derived based on a Trotter type factorization of the
classical Liouville propagator.
The new method is applied to a variety of simple one-dimensional
example problems and is shown to generate ergodic trajectories and correct
canonical distribution functions of both position and momentum.
The new method is further shown to lead to rapid convergence in molecular
dynamics based
calculations of path integrals.
The performance of the new
method in these examples is compared to that of another canonical dynamics
method, the
Nosé-Hoover chain method [G.J. Martyna, M.L. Klein and M.E. Tuckerman,
J. Chem. Phys. 97, 2635 (1992)]. The comparison demonstrates
the improvements afforded by the new method as a molecular dynamics tool.
Finally, when employed in molecular dynamics simulations of biological
macromolecules, the new method is shown to provide better energy
equipartitioning and temperature control and to lead to improved spatial
sampling over the Nosé-Hoover chain method in a realistic application.