1,545 research outputs found

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

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    Multipoles are the pieces we obtain by cutting some edges of a cubic graph. As a result of the cut, a multipole MM 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 M1M_1 and M2M_2 with the same number of semiedges, we say that M1M_1 is reducible to M2M_2 if the state set of M2M_2 is a non-empty subset of the state set of M1M_1 and M2M_2 has less vertices than M1M_1. The function v(m)v(m) is defined as the maximum number of vertices of an irreducible multipole with mm semiedges. The exact values of v(m)v(m) are only known for m≤5m\le 5. We prove that tree and cycle multipoles are irreducible and, as a byproduct, that v(m)v(m) has a linear lower bound

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

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    Heavy-particle cross sections differential in the momentum transferred to the target are investigated using the classical trajectory Monte Carlo method. with the 3.6  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

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    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

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    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

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    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 C6+^{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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