1,545 research outputs found

### Some results on the structure of multipoles in the study of snarks

Multipoles are the pieces we obtain by cutting some edges of a cubic graph.
As a result of the cut, a multipole $M$ has dangling edges with one free end,
which we call semiedges. Then, every 3-edge-coloring of a multipole induces a
coloring or state of its semiedges, which satisfies the Parity Lemma.
Multipoles have been extensively used in the study of snarks, that is, cubic
graphs which are not 3-edge-colorable. Some results on the states and structure
of the so-called color complete and color closed multipoles are presented. In
particular, we give lower and upper linear bounds on the minimum order of a
color complete multipole, and compute its exact number of states. Given two
multipoles $M_1$ and $M_2$ with the same number of semiedges, we say that $M_1$
is reducible to $M_2$ if the state set of $M_2$ is a non-empty subset of the
state set of $M_1$ and $M_2$ has less vertices than $M_1$. The function $v(m)$
is defined as the maximum number of vertices of an irreducible multipole with
$m$ semiedges. The exact values of $v(m)$ are only known for $m\le 5$. We prove
that tree and cycle multipoles are irreducible and, as a byproduct, that $v(m)$
has a linear lower bound

### Extreme Sensitivity of Differential Momentum Transfer Cross Sections to Target Atom Initial Conditions

Heavy-particle cross sections differential in the momentum transferred to the target are investigated using the classical trajectory Monte Carlo method. with the 3.6â€‰â€‰MeV/u Au53++He system as a test case, it is shown that these cross sections are extremely sensitive to the initial target temperature. In particular, when thermal motion is varied for one of the target\u27s initial momentum components between 0 and 25 K the absolute cross sections vary by orders of magnitude and, in addition, their relative shapes undergo major changes. We find that by setting one of the target\u27s transverse momenta to a temperature of 16 K, previously reported major discrepancies between theory and experiment are removed

### Infra-Red Finite Charge Propagation

The Coulomb gauge has a long history and many uses. It is especially useful
in bound state applications. An important feature of this gauge is that the
matter fields have an infra-red finite propagator in an on-shell
renormalisation scheme. This is, however, only the case if the renormalisation
point is chosen to be the static point on the mass shell, p = (m, 0, 0, 0). In
this letter we show how to extend this key property of the Coulomb gauge to an
arbitrary relativistic renormalisation point. This is achieved through the
introduction of a new class of gauges of which the Coulomb gauge is a limiting
case. A physical explanation for this result is given.Comment: 8 pages, plain TeX, to appear in Modern Physics Letters

### Defect CFTs and holographic multiverse

We investigate some aspects of a recent proposal for a holographic
description of the multiverse. Specifically, we focus on the implications on
the suggested duality of the fluctuations of a bubble separating two universes
with different cosmological constants. We do so by considering a similar
problem in a 2+1 CFT with a codimension one defect, obtained by an M5-brane
probe embedding in AdS_4x S^7, and studying its spectrum of fluctuations. Our
results suggest that the kind of behavior required by the spectrum of bubble
fluctuations is not likely to take place in defect CFTs with an AdS dual,
although it might be possible if the defect supports a non-unitary theory.Comment: 19 pages; v2: typos fixed, minor changes

### Semiclassical description of the kinematically complete experiments

Based on the semiclassical, impact parameter method a theoretical model is
constructed to calculate totally differential cross sections for single
ionization of helium by impact with fast C$^{6+}$ ions. Good agreement with the
experiment is achieved in the scattering plane, while in the perpendicular
plane a similar structure to that observed experimentally is obtained. The
contribution of different partial waves to the cross section is also
investigated.Comment: 9 pages, 6 figure

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