78,862 research outputs found
The stable braid group and the determinant of the Burau representation
This article gives certain fibre bundles associated to the braid groups which
are obtained from a translation as well as conjugation on the complex plane.
The local coefficient systems on the level of homology for these bundles are
given in terms of the determinant of the Burau representation.
De Concini, Procesi, and Salvetti [Topology 40 (2001) 739--751] considered
the cohomology of the n-th braid group B_n with local coefficients obtained
from the determinant of the Burau representation, H^*(B_n;Q[t^{+/-1}]). They
show that these cohomology groups are given in terms of cyclotomic fields.
This article gives the homology of the stable braid group with local
coefficients obtained from the determinant of the Burau representation. The
main result is an isomorphism
H_*(B_infty; F[t^{+/-1}])-->H_*(Omega^2S^3; F) for any field F where
Omega^2S^3 denotes the double loop space of the 3-connected cover of the
3-sphere. The methods are to translate the structure of H_*(B_n;F[t^{+/-1}]) to
one concerning the structure of the homology of certain function spaces where
the answer is computed.Comment: This is the version published by Geometry & Topology Monographs on 29
January 200
Spin dynamics of current driven single magnetic adatoms and molecules
A scanning tunneling microscope can probe the inelastic spin excitations of a
single magnetic atom in a surface via spin-flip assisted tunneling in which
transport electrons exchange spin and energy with the atomic spin. If the
inelastic transport time, defined as the average time elapsed between two
inelastic spin flip events, is shorter than the atom spin relaxation time, the
STM current can drive the spin out of equilibrium. Here we model this process
using rate equations and a model Hamiltonian that describes successfully spin
flip assisted tunneling experiments, including a single Mn atom, a Mn dimer and
Fe Phthalocyanine molecules. When the STM current is not spin polarized, the
non-equilibrium spin dynamics of the magnetic atom results in non-monotonic
curves. In the case of spin polarized STM current, the spin orientation
of the magnetic atom can be controlled parallel or anti-parallel to the
magnetic moment of the tip. Thus, spin polarized STM tips can be used both to
probe and to control the magnetic moment of a single atom.Comment: 15 pages, 12 figure
Backscattering and secondary-electron emission from metal targets of various thicknesses
Backscattering and secondary electron emission from metal targets of various thicknesse
Empirical equations for electron backscattering coefficients
Empirical equations for electron backscattering coefficient
Asymptotic Methods for Metal Oxide Semiconductor Field Effect Transistor Modeling
The behavior of metal oxide semiconductor field effect transistors (MOSFETs) with small aspect ratio and large doping levels is analyzed using formal perturbation techniques. Specifically, the influence of interface layers in the potential on the averaged channel conductivity is closely examined. The interface and internal layers that occur in the potential are resolved in the limit of large doping using the method of matched asymptotic expansions. This approach, together with other asymptotic techniques, provides both a pointwise description of the state variables as well as lumped current-voltage relations that vary uniformly across the various bias regimes. These current-voltage relations are derived for a variable doping model respresenting a particular class of devices
Constraints on Lorentz Invariance Violation from Fermi-Large Area Telescope Observations of Gamma-Ray Bursts
We analyze the MeV/GeV emission from four bright Gamma-Ray Bursts (GRBs)
observed by the Fermi-Large Area Telescope to produce robust, stringent
constraints on a dependence of the speed of light in vacuo on the photon energy
(vacuum dispersion), a form of Lorentz invariance violation (LIV) allowed by
some Quantum Gravity (QG) theories. First, we use three different and
complementary techniques to constrain the total degree of dispersion observed
in the data. Additionally, using a maximally conservative set of assumptions on
possible source-intrinsic spectral-evolution effects, we constrain any vacuum
dispersion solely attributed to LIV. We then derive limits on the "QG energy
scale" (the energy scale that LIV-inducing QG effects become important, E_QG)
and the coefficients of the Standard Model Extension. For the subluminal case
(where high energy photons propagate more slowly than lower energy photons) and
without taking into account any source-intrinsic dispersion, our most stringent
limits (at 95% CL) are obtained from GRB090510 and are E_{QG,1}>7.6 times the
Planck energy (E_Pl) and E_{QG,2}>1.3 x 10^11 GeV for linear and quadratic
leading order LIV-induced vacuum dispersion, respectively. These limits improve
the latest constraints by Fermi and H.E.S.S. by a factor of ~2. Our results
disfavor any class of models requiring E_{QG,1} \lesssim E_Pl.Comment: Accepted for publication by Physical Review
Note on the Kaplan-Yorke dimension and linear transport coefficients
A number of relations between the Kaplan-Yorke dimension, phase space
contraction, transport coefficients and the maximal Lyapunov exponents are
given for dissipative thermostatted systems, subject to a small external field
in a nonequilibrium stationary state. A condition for the extensivity of phase
space dimension reduction is given. A new expression for the transport
coefficients in terms of the Kaplan-Yorke dimension is derived. Alternatively,
the Kaplan-Yorke dimension for a dissipative macroscopic system can be
expressed in terms of the transport coefficients of the system. The agreement
with computer simulations for an atomic fluid at small shear rates is very
good.Comment: 12 pages, 5 figures, submitted to J. Stat. Phy
Basis-conjugating automorphisms of a free group and associated Lie algebras
Let F_n = denote the free group with generators {x_1,...,x_n}.
Nielsen and Magnus described generators for the kernel of the canonical
epimorphism from the automorphism group of F_n to the general linear group over
the integers. In particular among them are the automorphisms chi_{k,i} which
conjugate the generator x_k by the generator x_i leaving the x_j fixed for j
not k. A computation of the cohomology ring as well as the Lie algebra obtained
from the descending central series of the group generated by chi_{k,i} for i<k
is given here. Partial results are obtained for the group generated by all
chi_{k,i}.Comment: This is the version published by Geometry & Topology Monographs on 22
February 200
Comment on "Breakdown of the Internet under Intentional Attack"
We obtain the exact position of the percolation threshold in intentionally
damaged scale-free networks.Comment: 1 page, to appear in Phys. Rev. Let
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