8,926 research outputs found
A new two-dimensional lattice model that is "consistent around a cube"
For two-dimensional lattice equations one definition of integrability is that
the model can be naturally and consistently extended to three dimensions, i.e.,
that it is "consistent around a cube" (CAC). As a consequence of CAC one can
construct a Lax pair for the model. Recently Adler, Bobenko and Suris conducted
a search based on this principle and certain additional assumptions. One of
those assumptions was the "tetrahedron property", which is satisfied by most
known equations. We present here one lattice equation that satisfies the
consistency condition but does not have the tetrahedron property. Its Lax pair
is also presented and some basic properties discussed.Comment: 8 pages in LaTe
Optimal control of electromagnetic field using metallic nanoclusters
The dielectric properties of metallic nanoclusters in the presence of an
applied electromagnetic field are investigated using non-local linear response
theory. In the quantum limit we find a non-trivial dependence of the induced
field and charge distribution on the spatial separation between the clusters
and on the frequency of the driving field. Using a genetic algorithm, these
quantum functionalities are exploited to custom-design sub-wavelength lenses
with a frequency controlled switching capability.Comment: accepted for publication in New Journal of Physic
Difference schemes with point symmetries and their numerical tests
Symmetry preserving difference schemes approximating second and third order
ordinary differential equations are presented. They have the same three or
four-dimensional symmetry groups as the original differential equations. The
new difference schemes are tested as numerical methods. The obtained numerical
solutions are shown to be much more accurate than those obtained by standard
methods without an increase in cost. For an example involving a solution with a
singularity in the integration region the symmetry preserving scheme, contrary
to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure
Multiple-scale analysis of discrete nonlinear partial difference equations: the reduction of the lattice potential KdV
We consider multiple lattices and functions defined on them. We introduce
slow varying conditions for functions defined on the lattice and express the
variation of a function in terms of an asymptotic expansion with respect to the
slow varying lattices.
We use these results to perform the multiple--scale reduction of the lattice
potential Korteweg--de Vries equation.Comment: 17 pages. 1 figur
On the Integrability of the Discrete Nonlinear Schroedinger Equation
In this letter we present an analytic evidence of the non-integrability of
the discrete nonlinear Schroedinger equation, a well-known discrete evolution
equation which has been obtained in various contexts of physics and biology. We
use a reductive perturbation technique to show an obstruction to its
integrability.Comment: 4 pages, accepted in EP
Measurement of the Blackbody Radiation Shift of the 133Cs Hyperfine Transition in an Atomic Fountain
We used a Cs atomic fountain frequency standard to measure the Stark shift on
the ground state hyperfine transiton frequency in cesium (9.2 GHz) due to the
electric field generated by the blackbody radiation. The measures relative
shift at 300 K is -1.43(11)e-14 and agrees with our theoretical evaluation
-1.49(07)e-14. This value differs from the currently accepted one
-1.69(04)e-14. The difference has a significant implication on the accuracy of
frequency standards, in clocks comparison, and in a variety of high precision
physics tests such as the time stability of fundamental constants.Comment: 4 pages, 2 figures, 2 table
Multiscale reduction of discrete nonlinear Schroedinger equations
We use a discrete multiscale analysis to study the asymptotic integrability
of differential-difference equations. In particular, we show that multiscale
perturbation techniques provide an analytic tool to derive necessary
integrability conditions for two well-known discretizations of the nonlinear
Schroedinger equation.Comment: 12 page
Adaptive Design of Excitonic Absorption in Broken-Symmetry Quantum Wells
Adaptive quantum design is used to identify broken-symmetry quantum well
potential profiles with optical response properties superior to previous ad-hoc
solutions. This technique performs an unbiased stochastic search of
configuration space. It allows us to engineer many-body excitonic wave
functions and thus provides a new methodology to efficiently develop optimized
quantum confined Stark effect device structures.Comment: 4 pages, 3 encapsulated postscript figure
Integrability of Differential-Difference Equations with Discrete Kinks
In this article we discuss a series of models introduced by Barashenkov,
Oxtoby and Pelinovsky to describe some discrete approximations to the \phi^4
theory which preserve travelling kink solutions. We show, by applying the
multiple scale test that they have some integrability properties as they pass
the A_1 and A_2 conditions. However they are not integrable as they fail the
A_3 conditions.Comment: submitted to the Proceedings of the workshop "Nonlinear Physics:
Theory and Experiment.VI" in a special issue di Theoretical and Mathematical
Physic
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