6,811 research outputs found
Algebraic theories of brackets and related (co)homologies
A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets
in the category of modules over a commutative algebra is described. Some
related structures and (co)homology invariants are discussed, as well as
applications to geometry.Comment: 14 pages; v2: minor correction
Discretized rotation has infinitely many periodic orbits
For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by
(x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic
orbits.Comment: Revised after referee reports, and added a quantitative statemen
Electromagnetic wave refraction at an interface of a double wire medium
Plane-wave reflection and refraction at an interface with a double wire
medium is considered. The problem of additional boundary conditions (ABC) in
application to wire media is discussed and an ABC-free approach, known in the
solid state physics, is used. Expressions for the fields and Poynting vectors
of the refracted waves are derived. Directions and values of the power density
flow of the refracted waves are found and the conservation of the power flow
through the interface is checked. The difference between the results, given by
the conventional model of wire media and the model, properly taking into
account spatial dispersion, is discussed.Comment: 17 pages, 11 figure
One dimensional representations in quantum optics
The possibility of representing the quantum states of a harmonic oscillator not on the whole alpha-plane but on its one dimensional manifolds is considered. It is shown that a simple Gaussian distribution along a straight line describes a quadrature squeezed state while a similar Gaussian distribution along a circle leads to the amplitude squeezed state. The connection between the one dimensional representations and the usual Glauber representation is discussed
(Non)local Hamiltonian and symplectic structures, recursions, and hierarchies: a new approach and applications to the N=1 supersymmetric KdV equation
Using methods of math.DG/0304245 and [I.S.Krasil'shchik and P.H.M.Kersten,
Symmetries and recursion operators for classical and supersymmetric
differential equations, Kluwer, 2000], we accomplish an extensive study of the
N=1 supersymmetric Korteweg-de Vries equation. The results include: a
description of local and nonlocal Hamiltonian and symplectic structures, five
hierarchies of symmetries, the corresponding hierarchies of conservation laws,
recursion operators for symmetries and generating functions of conservation
laws. We stress that the main point of the paper is not just the results on
super-KdV equation itself, but merely exposition of the efficiency of the
geometrical approach and of the computational algorithms based on it.Comment: 16 pages, AMS-LaTeX, Xy-pic, dvi-file to be processed by dvips. v2:
nonessential improvements of exposition, title change
Sub-wavelength imaging: Resolution enhancement using metal wire gratings
An experimental evidence of subwavelength imaging with a "lens", which is a
uniaxial negative permittivity wire medium slab, is reported. The slab is
formed by gratings of long thin parallel conducting cylinders. Taking into
account the anisotropy and spatial dispersion in the wire medium we
theoretically show that there are no usual plasmons that could be exited on
surfaces of such a slab, and there is no resonant enhancement of evanescent
fields in the slab. The experimentally observed clear improvement of the
resolution in the presence of the slab is explained as filtering out the
harmonics with small wavenumbers. In other words, the wire gratings (the wire
medium) suppress strong traveling-mode components increasing the role of
evanescent waves in the image formation. This effect can be used in near-field
imaging and detection applications.Comment: 12 pages, 6 figure
The graded Jacobi algebras and (co)homology
Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in
the context of graded Jacobi brackets on graded commutative algebras. This
unifies varios concepts of graded Lie structures in geometry and physics. A
method of describing such structures by classical Lie algebroids via certain
gauging (in the spirit of E.Witten's gauging of exterior derivative) is
developed. One constructs a corresponding Cartan differential calculus (graded
commutative one) in a natural manner. This, in turn, gives canonical generating
operators for triangular Jacobi algebroids. One gets, in particular, the
Lichnerowicz-Jacobi homology operators associated with classical Jacobi
structures. Courant-Jacobi brackets are obtained in a similar way and use to
define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi
structure. All this offers a new flavour in understanding the
Batalin-Vilkovisky formalism.Comment: 20 pages, a few typos corrected; final version to be published in J.
Phys. A: Math. Ge
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