2,030 research outputs found
Mixed perturbative expansion: the validity of a model for the cascading
A new type of perturbative expansion is built in order to give a rigorous
derivation and to clarify the range of validity of some commonly used model
equations.
This model describes the evolution of the modulation of two short and
localized pulses, fundamental and second harmonic, propagating together in a
bulk uniaxial crystal with non-vanishing second order susceptibility
and interacting through the nonlinear effect known as ``cascading'' in
nonlinear optics.
The perturbative method mixes a multi-scale expansion with a power series
expansion of the susceptibility, and must be carefully adapted to the physical
situation. It allows the determination of the physical conditions under which
the model is valid: the order of magnitude of the walk-off, phase-mismatch,and
anisotropy must have determined values.Comment: arxiv version is already officia
Anyons, group theory and planar physics
Relativistic and nonrelativistic anyons are described in a unified formalism
by means of the coadjoint orbits of the symmetry groups in the free case as
well as when there is an interaction with a constant electromagnetic field. To
deal with interactions we introduce the extended Poincar\'e and Galilei Maxwell
groups.Comment: 22 pages, journal reference added, bibliography update
Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets
The dimensional reduction of the three-dimensional fermion-Chern-Simons model
(related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either
the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons
model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the
plane.Comment: 4 pages, Plain Tex, no figure
Lorentz Transformation from Symmetry of Reference Principle
The Lorentz Transformation is traditionally derived requiring the Principle
of Relativity and light-speed universality. While the latter can be relaxed,
the Principle of Relativity is seen as core to the transformation. The present
letter relaxes both statements to the weaker, Symmetry of Reference Principle.
Thus the resulting Lorentz transformation and its consequences (time
dilatation, length contraction) are, in turn, effects of how we manage space
and time.Comment: 2 page
(In)finite extensions of algebras from their Inonu-Wigner contractions
The way to obtain massive non-relativistic states from the Poincare algebra
is twofold. First, following Inonu and Wigner the Poincare algebra has to be
contracted to the Galilean one. Second, the Galilean algebra is to be extended
to include the central mass operator. We show that the central extension might
be properly encoded in the non-relativistic contraction. In fact, any
Inonu-Wigner contraction of one algebra to another, corresponds to an infinite
tower of abelian extensions of the latter. The proposed method is
straightforward and holds for both central and non-central extensions. Apart
from the Bargmann (non-zero mass) extension of the Galilean algebra, our list
of examples includes the Weyl algebra obtained from an extension of the
contracted SO(3) algebra, the Carrollian (ultra-relativistic) contraction of
the Poincare algebra, the exotic Newton-Hooke algebra and some others. The
paper is dedicated to the memory of Laurent Houart (1967-2011).Comment: 7 pages, revtex style; v2: Minor corrections, references added; v3:
Typos correcte
Finite-distance singularities in the tearing of thin sheets
We investigate the interaction between two cracks propagating in a thin
sheet. Two different experimental geometries allow us to tear sheets by
imposing an out-of-plane shear loading. We find that two tears converge along
self-similar paths and annihilate each other. These finite-distance
singularities display geometry-dependent similarity exponents, which we
retrieve using scaling arguments based on a balance between the stretching and
the bending of the sheet close to the tips of the cracks.Comment: 4 pages, 4 figure
Towards SDp-brane Quantization
The quantum mechanical analysis of the canonical hamiltonian description of
the effective action of a SDp-brane in bosonic ten dimensional Type II
supergravity in a homogeneous background is given. We find exact solutions for
the corresponding quantum theory by solving the Wheeler-deWitt equation in the
late-time limit of the rolling tachyon. The probability densities for several
values of p are shown and their possible interpretation is discussed. In the
process the effects of electromagnetic fields are also incorporated and it is
shown that in this case the interpretation of tachyon regarded as ``matter
clock'' is modified.Comment: 15 pages, 3 eps figures, revtex
Comments on Supergravity Description of S-branes
This is a note on the coupled supergravity-tachyon matter system, which has
been earlier proposed as a candidate for the effective space-time description
of S-branes. In particular, we study an ansatz with the maximal
ISO(p+1)xSO(8-p,1) symmetry, for general brane dimensionality p and homogeneous
brane distribution in transverse space \rho_\perp. A simple application of
singularity theorems shows that (for p \le 7) the most general solution with
these symmetries is always singular. (This invalidates a recent claim in the
literature.) We include a few general comments about the possibility of
describing the decay of unstable D-branes in purely gravitational terms.Comment: 19 pages, refs adde
Investigation of multiple pulsing and hysteresis phenomena in the erbium-doped double-clad fiber laser
We investigate both experimentally and theoretically the multiple pulsing behaviour of an erbium-doped double-clad fiber laser passively mode-locked through nonlinear polarization rotation. Hysteresis phenomena are found experimentally in both the normal and anomalous dispersion regime. Theoretical results are compared with experimental data allowing to fix the range of validity of the model
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