58 research outputs found
Weak Measurements of Light Chirality with a Plasmonic Slit
We examine, both experimentally and theoretically, an interaction of tightly
focused polarized light with a slit on a metal surface supporting
plasmon-polariton modes. Remarkably, this simple system can be highly sensitive
to the polarization of the incident light and offers a perfect
quantum-weak-measurement tool with a built-in post-selection in the
plasmon-polariton mode. We observe the plasmonic spin Hall effect in both
coordinate and momentum spaces which is interpreted as weak measurements of the
helicity of light with real and imaginary weak values determined by the input
polarization. Our experiment combines advantages of (i) quantum weak
measurements, (ii) near-field plasmonic systems, and (iii) high-numerical
aperture microscopy in employing spin-orbit interaction of light and probing
light chirality.Comment: 5 pages, 3 figure
On stochastic sea of the standard map
Consider a generic one-parameter unfolding of a homoclinic tangency of an
area preserving surface diffeomorphism. We show that for many parameters
(residual subset in an open set approaching the critical value) the
corresponding diffeomorphism has a transitive invariant set of full
Hausdorff dimension. The set is a topological limit of hyperbolic sets
and is accumulated by elliptic islands.
As an application we prove that stochastic sea of the standard map has full
Hausdorff dimension for sufficiently large topologically generic parameters.Comment: 36 pages, 5 figure
Non-hyperbolic ergodic measures with large support
We prove that there is a residual subset in
such that, for every , any homoclinic class of with
invariant one dimensional central bundle containing saddles of different
indices (i.e. with different dimensions of the stable invariant manifold)
coincides with the support of some invariant ergodic non-hyperbolic (one of the
Lyapunov exponents is equal to zero) measure of
Dynamics of some piecewise smooth Fermi-Ulam Models
We find a normal form which describes the high energy dynamics of a class of
piecewise smooth Fermi-Ulam ping pong models; depending on the value of a
single real parameter, the dynamics can be either hyperbolic or elliptic. In
the first case we prove that the set of orbits undergoing Fermi acceleration
has zero measure but full Hausdorff dimension. We also show that for almost
every orbit the energy eventually falls below a fixed threshold. In the second
case we prove that, generically, we have stable periodic orbits for arbitrarily
high energies, and that the set of Fermi accelerating orbits may have infinite
measure.Comment: 22 pages, 4 figure
Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect
We examine the spin-orbit coupling effects that appear when a wave carrying
intrinsic angular momentum interacts with a medium. The Berry phase is shown to
be a manifestation of the Coriolis effect in a non-inertial reference frame
attached to the wave. In the most general case, when both the direction of
propagation and the state of the wave are varied, the phase is given by a
simple expression that unifies the spin redirection Berry phase and the
Pancharatnam--Berry phase. The theory is supported by the experiment
demonstrating the spin-orbit coupling of electromagnetic waves via a surface
plasmon nano-structure. The measurements verify the unified geometric phase,
demonstrated by the observed polarization-dependent shift (spin-Hall effect) of
the waves.Comment: 4 pages, 3 figure
Multi-agent Model for Real Time Resource Allocation
Abstract. A large number of important applications are reducible to combinatorial models. Almost all of them are at least exponential complexÃty and cannot be solved in a traditional way. In the paper, we consider an agent -based approach to solve a class ofcomplex combinatorial problems in the area ofplanning and scheduling ofbounded resource al/ocation under real time and temporal constraints. The model ofthe problem is formulated in terms ofcontract al/ocation over a set of contractors and specified as an auction-based competÃtion of intelligent agents-contractors under agentmanager
supervision. The paper contributions are repeatable auction-based scheme of random search of admissible decisions: knowledge-based specification ofreal-time and temporal constraints that is used lo order of contrae! al/ocation from step lo step ofauction procedure; dynamic programming approach for forming strategy ofbargaining by agent-contractor
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Parametric Furstenberg Theorem on random products of SL(2,R) matrices
We consider random products of SL(2,R) matrices that depend on a parameter in a non-uniformly hyperbolic regime. We show that if the dependence on the parameter is monotone then almost surely the random product has upper (limsup) Lyapunov exponent that is equal to the value prescribed by the Furstenberg Theorem (and hence positive) for all parameters, but the lower (liminf) Lyapunov exponent is equal to zero for a dense Gδ set of parameters of zero Hausdorff dimension. As a byproduct of our methods, we provide a purely geometrical proof of Spectral Anderson Localization for discrete Schrödinger operators with random potentials (including the Anderson-Bernoulli model) on a one dimensional lattice
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