57,735 research outputs found

### Concentration dependence of the up- and down-conversion emission colours of Er3+-doped Y2O3: a time-resolved spectroscopy analysis

Er3+ energy transfer mechanisms and their influence on the dynamics and emission colours are considered for upconversion and downconversion regimes.</jats:p

### From Topology to Generalised Dimensional Reduction

In the usual procedure for toroidal Kaluza-Klein reduction, all the
higher-dimensional fields are taken to be independent of the coordinates on the
internal space. It has recently been observed that a generalisation of this
procedure is possible, which gives rise to lower-dimensional ``massive''
supergravities. The generalised reduction involves allowing gauge potentials in
the higher dimension to have an additional linear dependence on the toroidal
coordinates. In this paper, we show that a much wider class of generalised
reductions is possible, in which higher-dimensional potentials have additional
terms involving differential forms on the internal manifold whose exterior
derivatives yield representatives of certain of its cohomology classes. We
consider various examples, including the generalised reduction of M-theory and
type II strings on K3, Calabi-Yau and 7-dimensional Joyce manifolds. The
resulting massive supergravities support domain-wall solutions that arise by
the vertical dimensional reduction of higher-dimensional solitonic p-branes and
intersecting p-branes.Comment: Latex, 24 pages, no figures, typo corrected, reference added and
discussion of duality extende

### Lie-Poisson Deformation of the Poincar\'e Algebra

We find a one parameter family of quadratic Poisson structures on ${\bf
R}^4\times SL(2,C)$ which satisfies the property {\it a)} that it is preserved
under the Lie-Poisson action of the Lorentz group, as well as {\it b)} that it
reduces to the standard Poincar\'e algebra for a particular limiting value of
the parameter. (The Lie-Poisson transformations reduce to canonical ones in
that limit, which we therefore refer to as the `canonical limit'.) Like with
the Poincar\'e algebra, our deformed Poincar\'e algebra has two Casimir
functions which we associate with `mass' and `spin'. We parametrize the
symplectic leaves of ${\bf R}^4\times SL(2,C)$ with space-time coordinates,
momenta and spin, thereby obtaining realizations of the deformed algebra for
the cases of a spinless and a spinning particle. The formalism can be applied
for finding a one parameter family of canonically inequivalent descriptions of
the photon.Comment: Latex file, 26 page

### Brownian motion of solitons in a Bose-Einstein Condensate

For the first time, we observed and controlled the Brownian motion of
solitons. We launched solitonic excitations in highly elongated $^{87}\rm{Rb}$
BECs and showed that a dilute background of impurity atoms in a different
internal state dramatically affects the soliton. With no impurities and in
one-dimension (1-D), these solitons would have an infinite lifetime, a
consequence of integrability. In our experiment, the added impurities scatter
off the much larger soliton, contributing to its Brownian motion and decreasing
its lifetime. We describe the soliton's diffusive behavior using a quasi-1-D
scattering theory of impurity atoms interacting with a soliton, giving
diffusion coefficients consistent with experiment.Comment: 4 figure

### Computing the Girth of a Planar Graph in Linear Time

The girth of a graph is the minimum weight of all simple cycles of the graph.
We study the problem of determining the girth of an n-node unweighted
undirected planar graph. The first non-trivial algorithm for the problem, given
by Djidjev, runs in O(n^{5/4} log n) time. Chalermsook, Fakcharoenphol, and
Nanongkai reduced the running time to O(n log^2 n). Weimann and Yuster further
reduced the running time to O(n log n). In this paper, we solve the problem in
O(n) time.Comment: 20 pages, 7 figures, accepted to SIAM Journal on Computin

### Lorentz Transformations as Lie-Poisson Symmetries

We write down the Poisson structure for a relativistic particle where the
Lorentz group does not act canonically, but instead as a Poisson-Lie group. In
so doing we obtain the classical limit of a particle moving on a noncommutative
space possessing $SL_q(2,C)$ invariance. We show that if the standard mass
shell constraint is chosen for the Hamiltonian function, then the particle
interacts with the space-time. We solve for the trajectory and find that it
originates and terminates at singularities.Comment: 18 page

### Casimir Effect for the Piecewise Uniform String

The Casimir energy for the transverse oscillations of a piecewise uniform
closed string is calculated. In its simplest version the string consists of two
parts I and II having in general different tension and mass density, but is
always obeying the condition that the velocity of sound is equal to the
velocity of light. The model, first introduced by Brevik and Nielsen in 1990,
possesses attractive formal properties implying that it becomes easily
regularizable by several methods, the most powerful one being the contour
integration method. We also consider the case where the string is divided into
2N pieces, of alternating type-I and type-II material. The free energy at
finite temperature, as well as the Hagedorn temperature, are found. Finally, we
make some remarks on the relationship between this kind of theory and the
theory of quantum star graphs, recently considered by Fulling et al.Comment: 10 pages, 1 figure, Submitted to the volume "Cosmology, Quantum
Vacuum, and Zeta Functions", in honour of Professor Emilio Elizalde on the
occasion of his 60th birthda

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