8,275 research outputs found
Geometric phases and anholonomy for a class of chaotic classical systems
Berry's phase may be viewed as arising from the parallel transport of a
quantal state around a loop in parameter space. In this Letter, the classical
limit of this transport is obtained for a particular class of chaotic systems.
It is shown that this ``classical parallel transport'' is anholonomic ---
transport around a closed curve in parameter space does not bring a point in
phase space back to itself --- and is intimately related to the Robbins-Berry
classical two-form.Comment: Revtex, 11 pages, no figures
Melting-freezing cycles in a relatively sheared pair of crystalline monolayers
The nonequilibrium dynamical behaviour that arises when two ordered
two-dimensional monolayers of particles are sheared over each other is studied
in Brownian dynamics simulations. A curious sequence of nonequilibrium states
is observed as the driving rate is increased, the most striking of which is a
sliding state with irregular alternation between disordered and ordered states.
We comment on possible mechanisms underlying these cycles, and experiments that
could observe them.Comment: 7 pages, 8 figures, minor changes in text and figures, references
adde
Quantum evolution across singularities: the case of geometrical resolutions
We continue the study of time-dependent Hamiltonians with an isolated
singularity in their time dependence, describing propagation on singular
space-times. In previous work, two of us have proposed a "minimal subtraction"
prescription for the simplest class of such systems, involving Hamiltonians
with only one singular term. On the other hand, Hamiltonians corresponding to
geometrical resolutions of space-time tend to involve multiple operator
structures (multiple types of dependence on the canonical variables) in an
essential way.
We consider some of the general properties of such (near-)singular
Hamiltonian systems, and further specialize to the case of a free scalar field
on a two-parameter generalization of the null-brane space-time. We find that
the singular limit of free scalar field evolution exists for a discrete subset
of the possible values of the two parameters. The coordinates we introduce
reveal a peculiar reflection property of scalar field propagation on the
generalized (as well as the original) null-brane. We further present a simple
family of pp-wave geometries whose singular limit is a light-like hyperplane
(discontinuously) reflecting the positions of particles as they pass through
it.Comment: 25 pages, 1 figur
Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints
We consider the bilevel optimisation approach proposed by De Los Reyes,
Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation
(TV) denoising model featuring for multiple noise distributions. In
applications, the use of databases (dictionaries) allows an accurate estimation
of the parameters, but reflects in high computational costs due to the size of
the databases and to the nonsmooth nature of the PDE constraints. To overcome
this computational barrier we propose an optimisation algorithm that by
sampling dynamically from the set of constraints and using a quasi-Newton
method, solves the problem accurately and in an efficient way
Complex Periodic Orbits and Tunnelling in Chaotic Potentials
We derive a trace formula for the splitting-weighted density of states
suitable for chaotic potentials with isolated symmetric wells. This formula is
based on complex orbits which tunnel through classically forbidden barriers.
The theory is applicable whenever the tunnelling is dominated by isolated
orbits, a situation which applies to chaotic systems but also to certain
near-integrable ones. It is used to analyse a specific two-dimensional
potential with chaotic dynamics. Mean behaviour of the splittings is predicted
by an orbit with imaginary action. Oscillations around this mean are obtained
from a collection of related orbits whose actions have nonzero real part
Friction Laws for Elastic Nano-Scale Contacts
The effect of surface curvature on the law relating frictional forces F with
normal load L is investigated by molecular dynamics simulations as a function
of surface symmetry, adhesion, and contamination. Curved, non-adhering, dry,
commensurate surfaces show a linear dependency, F proportional to L, similar to
dry flat commensurate or amorphous surfaces and macroscopic surfaces. In
contrast, curved, non-adhering, dry, amorphous surfaces show F proportional to
L^(2/3) similar to friction force microscopes. In our model, adhesive effects
are most adequately described by the Hertz plus offset model, as the
simulations are confined to small contact radii. Curved lubricated or
contaminated surfaces show again different behavior; details depend on how much
of the contaminant gets squeezed out of the contact. Also, it is seen that the
friction force in the lubricated case is mainly due to atoms at the entrance of
the tip.Comment: 7 pages, 5 figures, submitted to Europhys. Let
Toward the End of Time
The null-brane space-time provides a simple model of a big crunch/big bang
singularity. A non-perturbative definition of M-theory on this space-time was
recently provided using matrix theory. We derive the fermion couplings for this
matrix model and study the leading quantum effects. These effects include
particle production and a time-dependent potential. Our results suggest that as
the null-brane develops a big crunch singularity, the usual notion of
space-time is replaced by an interacting gluon phase. This gluon phase appears
to constitute the end of our conventional picture of space and time.Comment: 31 pages, reference adde
A Matrix Model for the Null-Brane
The null-brane background is a simple smooth 1/2 BPS solution of string
theory. By tuning a parameter, this background develops a big crunch/big bang
type singularity. We construct the DLCQ description of this space-time in terms
of a Yang-Mills theory on a time-dependent space-time. Our dual Matrix
description provides a non-perturbative framework in which the fate of both
(null) time, and the string S-matrix can be studied.Comment: 26 pages, LaTeX; references adde
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