6,292 research outputs found
On universal unfoldings of certain real functions on a Banach space
The aim of this article is to prove a result which has been thought true for some time. Roughly speaking, if you take a universal unfolding of a germ in finitely many variables, and add to it a non-degenerate quadratic form on an infinite-dimensional space, you still have a universal unfoldin
Breathers in the weakly coupled topological discrete sine-Gordon system
Existence of breather (spatially localized, time periodic, oscillatory)
solutions of the topological discrete sine-Gordon (TDSG) system, in the regime
of weak coupling, is proved. The novelty of this result is that, unlike the
systems previously considered in studies of discrete breathers, the TDSG system
does not decouple into independent oscillator units in the weak coupling limit.
The results of a systematic numerical study of these breathers are presented,
including breather initial profiles and a portrait of their domain of existence
in the frequency-coupling parameter space. It is found that the breathers are
uniformly qualitatively different from those found in conventional spatially
discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely
rewritte
Inelastic fingerprints of hydrogen contamination in atomic gold wire systems
We present series of first-principles calculations for both pure and hydrogen
contaminated gold wire systems in order to investigate how such impurities can
be detected. We show how a single H atom or a single H2 molecule in an atomic
gold wire will affect forces and Au-Au atom distances under elongation. We
further determine the corresponding evolution of the low-bias conductance as
well as the inelastic contributions from vibrations. Our results indicate that
the conductance of gold wires is only slightly reduced from the conductance
quantum G0=2e^2/h by the presence of a single hydrogen impurity, hence making
it difficult to use the conductance itself to distinguish between various
configurations. On the other hand, our calculations of the inelastic signals
predict significant differences between pure and hydrogen contaminated wires,
and, importantly, between atomic and molecular forms of the impurity. A
detailed characterization of gold wires with a hydrogen impurity should
therefore be possible from the strain dependence of the inelastic signals in
the conductance.Comment: 5 pages, 3 figures, Contribution to ICN+T2006, Basel, Switzerland,
July-August 200
Inverse Ising inference using all the data
We show that a method based on logistic regression, using all the data,
solves the inverse Ising problem far better than mean-field calculations
relying only on sample pairwise correlation functions, while still
computationally feasible for hundreds of nodes. The largest improvement in
reconstruction occurs for strong interactions. Using two examples, a diluted
Sherrington-Kirkpatrick model and a two-dimensional lattice, we also show that
interaction topologies can be recovered from few samples with good accuracy and
that the use of -regularization is beneficial in this process, pushing
inference abilities further into low-temperature regimes.Comment: 5 pages, 2 figures. Accepted versio
Static axisymmetric space-times with prescribed multipole moments
In this article we develop a method of finding the static axisymmetric
space-time corresponding to any given set of multipole moments. In addition to
an implicit algebraic form for the general solution, we also give a power
series expression for all finite sets of multipole moments. As conjectured by
Geroch we prove in the special case of axisymmetry, that there is a static
space-time for any given set of multipole moments subject to a (specified)
convergence criterion. We also use this method to confirm a conjecture of
Hernandez-Pastora and Martin concerning the monopole-quadropole solution.Comment: 14 page
Reheating induced by competing decay modes
We address the problem of studying the decay of the inflaton field to
another scalar field through parametric resonance in the case of a
coupling that involves several decay modes. This amounts to the presence of
extra harmonic terms in the perturbation of the field dynamics. For the
case of two frequencies we compute the geometry of the resonance regions, which
is significantly altered due to the presence of non-cuspidal resonance regions
associated to higher harmonics and to the emergence of instability `pockets'.
We discuss the effect of this change in the efficiency of the energy transfer
process for the simplest case of a coupling given by a combination of the two
interaction terms of homogeneous degree usually considered in the literature.
We find that the presence of higher harmonics has limited cosmological
implications.Comment: 14 pages, 4 figures Added references. Corrected typo
High Energy Quark-Antiquark Elastic scattering with Mesonic Exchange
We studies the high energy elastic scattering of quark anti-quark with an
exchange of a mesonic state in the channel with .
Both the normalization factor and the Regge trajectory can be calculated in
PQCD in cases of fixed (non-running) and running coupling constant. The
dependence of the Regge trajectory on the coupling constant is highly
non-linear and the trajectory is of order of in the interesting physical
range.Comment: 29 page
More on coupling coefficients for the most degenerate representations of SO(n)
We present explicit closed-form expressions for the general group-theoretical
factor appearing in the alpha-topology of a high-temperature expansion of
SO(n)-symmetric lattice models. This object, which is closely related to
6j-symbols for the most degenerate representation of SO(n), is discussed in
detail.Comment: 9 pages including 1 table, uses IOP macros Update of Introduction and
Discussion, References adde
Quantum Structure of Space Near a Black Hole Horizon
We describe a midi-superspace quantization scheme for generic single horizon
black holes in which only the spatial diffeomorphisms are fixed. The remaining
Hamiltonian constraint yields an infinite set of decoupled eigenvalue
equations: one at each spatial point. The corresponding operator at each point
is the product of the outgoing and ingoing null convergences, and describes the
scale invariant quantum mechanics of a particle moving in an attractive
potential. The variable that is analoguous to particle position is the
square root of the conformal mode of the metric. We quantize the theory via
Bohr quantization, which by construction turns the Hamiltonian constraint
eigenvalue equation into a finite difference equation. The resulting spectrum
gives rise to a discrete spatial topology exterior to the horizon. The spectrum
approaches the continuum in the asymptotic region.Comment: References added and typos corrected. 21 pages, 1 figur
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