Seminar Fizičkog odsjeka / Seminar of the Department of Physics

Imaginary-time path-integrals or ``ring-polymers" are a
long-established practical technique for simulating quantum Boltzmann
statistics. More recently, they have also been used to simulate
real-time dynamics, using the centroid molecular dynamics (CMD) and
(thermostatted) ring-polymer molecular dynamics ((T)RPMD) methods. Here,
we show that the theoretical basis of CMD and RPMD is a classical
dynamics which arises when the exact quantum dynamics is represented
using path-integrals and is coarse-grained to make it a smooth and
differentiable function of imaginary-time. This ``Matsubara" dynamics
cannot be used as a practical method (because of a severe sign problem),
but can be used to critique and refine heuristic methods such as CMD and
RPMD, which turn out to be approximations to Matsubara dynamics that
avoid the phase. In particular, we will show how to extend quantum
simulations of the infrared spectrum of liquid water and ice to lower
temperatures (150 K) than hitherto possible.