1,337 research outputs found
Efficient computation of matched solutions of the Kapchinskij-Vladimirskij envelope equations for periodic focusing lattices
A new iterative method is developed to numerically calculate the periodic,
matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV)
equations describing the transverse evolution of a beam in a periodic, linear
focusing lattice of arbitrary complexity. Implementation of the method is
straightforward. It is highly convergent and can be applied to all usual
parameterizations of the matched envelope solutions. The method is applicable
to all classes of linear focusing lattices without skew couplings, and also
applies to all physically achievable system parameters -- including where the
matched beam envelope is strongly unstable. Example applications are presented
for periodic solenoidal and quadrupole focusing lattices. Convergence
properties are summarized over a wide range of system parameters.Comment: 20 pages, 5 figures, Mathematica source code provide
Effect of transient pinning on stability of drops sitting on an inclined plane
We report on new instabilities of the quasi-static equilibrium of water drops
pinned by a hydrophobic inclined substrate. The contact line of a statically
pinned drop exhibits three transitions of partial depinning: depinning of the
advancing and receding parts of the contact line and depinning of the entire
contact line leading to the drop's translational motion. We find a region of
parameters where the classical Macdougall-Ockrent-Frenkel approach fails to
estimate the critical volume of the statically pinned inclined drop
Renormalized Equilibria of a Schloegl Model Lattice Gas
A lattice gas model for Schloegl's second chemical reaction is described and
analyzed. Because the lattice gas does not obey a semi-detailed-balance
condition, the equilibria are non-Gibbsian. In spite of this, a self-consistent
set of equations for the exact homogeneous equilibria are described, using a
generalized cluster-expansion scheme. These equations are solved in the
two-particle BBGKY approximation, and the results are compared to numerical
experiment. It is found that this approximation describes the equilibria far
more accurately than the Boltzmann approximation. It is also found, however,
that spurious solutions to the equilibrium equations appear which can only be
removed by including effects due to three-particle correlations.Comment: 21 pages, REVTe
Guiding of cold atoms by a red-detuned laser beam of moderate power
We report measurements on the guiding of cold Rb atoms from a
magneto-optical trap by a continuous light beam over a vertical distance of 6.5
mm. For moderate laser power (85 mW) we are able to capture around 40% of
the cold atoms. Although the guide is red-detuned, the optical scattering rate
at this detuning (70 GHz) is acceptably low. For lower detuning (30
GHz) a larger fraction was guided but radiation pressure starts to push the
atoms upward, effectively lowering the acceleration due to gravity. The
measured guided fraction agrees well with an analytical model.Comment: final version, 6 pages, incl. 6 figure
Topological phase transition in a RNA model in the de Gennes regime
We study a simplified model of the RNA molecule proposed by G. Vernizzi, H.
Orland and A. Zee in the regime of strong concentration of positive ions in
solution. The model considers a flexible chain of equal bases that can pairwise
interact with any other one along the chain, while preserving the property of
saturation of the interactions. In the regime considered, we observe the
emergence of a critical temperature T_c separating two phases that can be
characterized by the topology of the predominant configurations: in the large
temperature regime, the dominant configurations of the molecule have very large
genera (of the order of the size of the molecule), corresponding to a complex
topology, whereas in the opposite regime of low temperatures, the dominant
configurations are simple and have the topology of a sphere. We determine that
this topological phase transition is of first order and provide an analytic
expression for T_c. The regime studied for this model exhibits analogies with
that for the dense polymer systems studied by de GennesComment: 15 pages, 4 figure
Fundamental Weights, Permutation Weights and Weyl Character Formula
For a finite Lie algebra of rank N, the Weyl orbits
of strictly dominant weights contain number of
weights where is the dimension of its Weyl group . For any
, there is a very peculiar subset for
which we always have For
any dominant weight , the elements of are called
{\bf Permutation Weights}.
It is shown that there is a one-to-one correspondence between elements of
and where is the Weyl vector of .
The concept of signature factor which enters in Weyl character formula can be
relaxed in such a way that signatures are preserved under this one-to-one
correspondence in the sense that corresponding permutation weights have the
same signature. Once the permutation weights and their signatures are specified
for a dominant , calculation of the character for
irreducible representation will then be provided by
multiplicity rules governing generalized Schur functions. The main idea is
again to express everything in terms of the so-called {\bf Fundamental Weights}
with which we obtain a quite relevant specialization in applications of Weyl
character formula.Comment: 6 pages, no figures, TeX, as will appear in Journal of Physics
A:Mathematical and Genera
Towards the theory of integrable hyperbolic equations of third order
The examples are considered of integrable hyperbolic equations of third order
with two independent variables. In particular, an equation is found which
admits as evolutionary symmetries the Krichever--Novikov equation and the
modified Landau--Lifshitz system. The problem of choice of dynamical variables
for the hyperbolic equations is discussed.Comment: 22
Quantum repeaters and quantum key distribution: analysis of secret key rates
We analyze various prominent quantum repeater protocols in the context of
long-distance quantum key distribution. These protocols are the original
quantum repeater proposal by Briegel, D\"ur, Cirac and Zoller, the so-called
hybrid quantum repeater using optical coherent states dispersively interacting
with atomic spin qubits, and the Duan-Lukin-Cirac-Zoller-type repeater using
atomic ensembles together with linear optics and, in its most recent extension,
heralded qubit amplifiers. For our analysis, we investigate the most important
experimental parameters of every repeater component and find their minimally
required values for obtaining a nonzero secret key. Additionally, we examine in
detail the impact of device imperfections on the final secret key rate and on
the optimal number of rounds of distillation when the entangled states are
purified right after their initial distribution.Comment: Published versio
Coupled-Map Modeling of One-Dimensional Traffic Flow
We propose a new model of one-dimensional traffic flow using a coupled map
lattice. In the model, each vehicle is assigned a map and changes its velocity
according to it. A single map is designed so as to represent the motion of a
vehicle properly, and the maps are coupled to each other through the headway
distance. By simulating the model, we obtain a plot of the flow against the
concentration similar to the observed data in real traffic flows. Realistic
traffic jam regions are observed in space-time trajectories.Comment: 5 postscript figures available upon reques
Two-State Spectral-Free Solutions of Frenkel-Moore Simplex Equation
Whilst many solutions have been found for the Quantum Yang-Baxter Equation
(QYBE), there are fewer known solutions available for its higher dimensional
generalizations: Zamolodchikov's tetrahedron equation (ZTE) and Frenkel and
Moore's simplex equation (FME). In this paper, we present families of solutions
to FME which may help us to understand more about higher dimensional
generalization of QYBE.Comment: LaTeX file. Require macros: cite.sty and subeqnarray.sty to process.
To appear in J. Phys. A: Math. and Ge
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