Hey Everyone,
The time has come for me, Ryan Babbush, the group meeting announcer,
to give group meeting. This Friday at 2:30 I'll be explaining work
that John Parkhill and I have been doing regarding the use of
functionals to cheaply reproduce results of path integral statistical
mechanics. An abstract is provided below.
============================
Force-Field Functional Theory:
A Uniqueness and Existence Proof for Classical Force-Fields
which Reproduce Equilibrium Quantum Distributions
Feynman and Hibbs were the first to variationally determine an
effective classical potential which
could be integrated classically to approximate the exact quantum
partition function given by the
path integral formulation of statistical mechanics. Since then, many
have presented methods which
more accurately approximate the effective classical potential and some
of these approximations are
used regularly for molecular dynamics. We prove that there always
exists an unique operator which
maps the classical potential to an effective classical potential which
samples the exact quantum
ensemble equilibrium density and all related equilibrium averages.
Furthermore, we show that this
operator is a linear operator to at least second order in the
potential. These result suggests a
systematic avenue for finding "force-field functionals" with a
motivation similar in spirit to the
powerful ideas and approximations stemming from density functional theory.
--
Ryan Babbush | PhD Student in Chemistry
(949) 331-3943 | babbush(a)fas.harvard.edu
Harvard University | Aspuru-Guzik Research Group
12 Oxford Street, Box 400 | Cambridge, MA 02138
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