14,348 research outputs found
A Lattice Simulation of the SU(2) Vacuum Structure
In this article we analyze the vacuum structure of pure SU(2) Yang-Mills
using non-perturbative techniques. Monte Carlo simulations are performed for
the lattice gauge theory with external sources to obtain the effective
potential. Evidence from the lattice gauge theory indicating the presence of
the unstable mode in the effective potential is reported.Comment: 12 pages, latex with revtex style, figures avalable by e-mail:
[email protected]
Lie discrete symmetries of lattice equations
We extend two of the methods previously introduced to find discrete
symmetries of differential equations to the case of difference and
differential-difference equations. As an example of the application of the
methods, we construct the discrete symmetries of the discrete Painlev\'e I
equation and of the Toda lattice equation
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
Lie Symmetries and Exact Solutions of First Order Difference Schemes
We show that any first order ordinary differential equation with a known Lie
point symmetry group can be discretized into a difference scheme with the same
symmetry group. In general, the lattices are not regular ones, but must be
adapted to the symmetries considered. The invariant difference schemes can be
so chosen that their solutions coincide exactly with those of the original
differential equation.Comment: Minor changes and journal-re
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
Fast and robust two-qubit gates for scalable ion trap quantum computing
We propose a new concept for a two-qubit gate operating on a pair of trapped
ions based on laser coherent control techniques. The gate is insensitive to the
temperature of the ions, works also outside the Lamb-Dicke regime, requires no
individual addressing by lasers, and can be orders of magnitude faster than the
trap period
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
Discrete derivatives and symmetries of difference equations
We show on the example of the discrete heat equation that for any given
discrete derivative we can construct a nontrivial Leibniz rule suitable to find
the symmetries of discrete equations. In this way we obtain a symmetry Lie
algebra, defined in terms of shift operators, isomorphic to that of the
continuous heat equation.Comment: submitted to J.Phys. A 10 Latex page
Multiscale expansion and integrability properties of the lattice potential KdV equation
We apply the discrete multiscale expansion to the Lax pair and to the first
few symmetries of the lattice potential Korteweg-de Vries equation. From these
calculations we show that, like the lowest order secularity conditions give a
nonlinear Schroedinger equation, the Lax pair gives at the same order the
Zakharov and Shabat spectral problem and the symmetries the hierarchy of point
and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007
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