1,203,426 research outputs found
Phase Transition in Two Species Zero-Range Process
We study a zero-range process with two species of interacting particles. We
show that the steady state assumes a simple factorised form, provided the
dynamics satisfy certain conditions, which we derive. The steady state exhibits
a new mechanism of condensation transition wherein one species induces the
condensation of the other. We study this mechanism for a specific choice of
dynamics.Comment: 8 pages, 3 figure
How to remove the spurious resonances from ring polymer molecular dynamics
Two of the most successful methods that are presently available for
simulating the quantum dynamics of condensed phase systems are centroid
molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite
their conceptual differences, practical implementations of these methods differ
in just two respects: the choice of the Parrinello-Rahman mass matrix and
whether or not a thermostat is applied to the internal modes of the ring
polymer during the dynamics. Here we explore a method which is halfway between
the two approximations: we keep the path integral bead masses equal to the
physical particle masses but attach a Langevin thermostat to the internal modes
of the ring polymer during the dynamics. We justify this by showing
analytically that the inclusion of an internal mode thermostat does not affect
any of the desirable features of RPMD: thermostatted RPMD (TRPMD) is equally
valid with respect to everything that has actually been proven about the method
as RPMD itself. In particular, because of the choice of bead masses, the
resulting method is still optimum in the short-time limit, and the transition
state approximation to its reaction rate theory remains closely related to the
semiclassical instanton approximation in the deep quantum tunneling regime. In
effect, there is a continuous family of methods with these properties,
parameterised by the strength of the Langevin friction. Here we explore
numerically how the approximation to quantum dynamics depends on this friction,
with a particular emphasis on vibrational spectroscopy. We find that a broad
range of frictions approaching optimal damping give similar results, and that
these results are immune to both the resonance problem of RPMD and the
curvature problem of CMD
Condensation Transitions in Two Species Zero-Range Process
We study condensation transitions in the steady state of a zero-range process
with two species of particles. The steady state is exactly soluble -- it is
given by a factorised form provided the dynamics satisfy certain constraints --
and we exploit this to derive the phase diagram for a quite general choice of
dynamics. This phase diagram contains a variety of new mechanisms of condensate
formation, and a novel phase in which the condensate of one of the particle
species is sustained by a `weak' condensate of particles of the other species.
We also demonstrate how a single particle of one of the species (which plays
the role of a defect particle) can induce Bose-Einstein condensation above a
critical density of particles of the other species.Comment: 17 pages, 4 Postscript figure
Information-geometric Markov Chain Monte Carlo methods using Diffusions
Recent work incorporating geometric ideas in Markov chain Monte Carlo is
reviewed in order to highlight these advances and their possible application in
a range of domains beyond Statistics. A full exposition of Markov chains and
their use in Monte Carlo simulation for Statistical inference and molecular
dynamics is provided, with particular emphasis on methods based on Langevin
diffusions. After this geometric concepts in Markov chain Monte Carlo are
introduced. A full derivation of the Langevin diffusion on a Riemannian
manifold is given, together with a discussion of appropriate Riemannian metric
choice for different problems. A survey of applications is provided, and some
open questions are discussed.Comment: 22 pages, 2 figure
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