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Topological aspects of quantum spin Hall effect in graphene: Z topological order and spin Chern number
For generic time-reversal invariant systems with spin-orbit couplings, we
clarify a close relationship between the Z topological order and the spin
Chern number proposed by Kane and Mele and by Sheng {\it et al.}, respectively,
in the quantum spin Hall effect. It turns out that a global gauge
transformation connects different spin Chern numbers (even integers) modulo 4,
which implies that the spin Chern number and the Z topological order yield
the same classification. We present a method of computing spin Chern numbers
and demonstrate it in single and double plane of graphene.Comment: 5 pages, 3 figure
Invited review: KPZ. Recent developments via a variational formulation
Recently, a variational approach has been introduced for the paradigmatic
Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together
with the functional Taylor expansion that the KPZ nonequilibrium potential
(NEP) admits. Such expansion becomes naturally truncated at third order, giving
rise to a nonlinear stochastic partial differential equation to be regarded as
a gradient-flow counterpart to the KPZ equation. A dynamic renormalization
group analysis at one-loop order of this new mesoscopic model yields the KPZ
scaling relation alpha+z=2, as a consequence of the exact cancelation of the
different contributions to vertex renormalization. This result is quite
remarkable, considering the lower degree of symmetry of this equation, which is
in particular not Galilean invariant. In addition, this scheme is exploited to
inquire about the dynamical behavior of the KPZ equation through a
path-integral approach. Each of these aspects offers novel points of view and
sheds light on particular aspects of the dynamics of the KPZ equation.Comment: 16 pages, 2 figure
Tests of non-standard electroweak couplings of right-handed quarks
The standard model can be interpreted as the leading order of a Low-Energy
Effective Theory (LEET) invariant under a higher non linearly realized symmetry
equipped with a systematic power
counting. Within the minimal version of this ``not quite decoupling'' LEET, the
dominant non-standard effect appears at next-to-leading order (NLO) and is a
modification of the couplings of fermions to W and Z. In particular, the
coupling of right-handed quarks to Z is modified and a direct coupling of
right-handed quarks to W emerges. Charged right-handed lepton currents are
forbidden by an additional discrete symmetry in the lepton sector originally
designed to suppress Dirac neutrino masses. A complete NLO analysis of
experimental constraints on these modified couplings is presented. Concerning
couplings of light quarks, the interface of the electroweak tests with QCD
aspects is discussed in detail.Comment: 56 pages, 14 figures, v2: references added, minor modifications in
the text, accepted for publication in JHE
Assessing the accuracy of Hartree-Fock-Bogoliubov calculations by use of mass relations
The accuracy of three different sets of Hartree-Fock-Bogoliubov calculations
of nuclear binding energies is systematically evaluated. To emphasize minor
fluctuations, a second order, four-point mass relation, which almost completely
eliminates smooth aspects of the binding energy, is introduced. Applying this
mass relation yields more scattered results for the calculated binding
energies. By examining the Gaussian distributions of the non-smooth aspects
which remain, structural differences can be detected between measured and
calculated binding energies. Substructures in regions of rapidly changing
deformation, specifically around and , are clearly
seen for the measured values, but are missing from the calculations. A similar
three-point mass relation is used to emphasize odd-even effects. A clear
decrease with neutron excess is seen continuing outside the experimentally
known region for the calculations.Comment: 13 pages, 9 figures, published versio
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