36,778 research outputs found
Einstein Manifolds As Yang-Mills Instantons
It is well-known that Einstein gravity can be formulated as a gauge theory of
Lorentz group where spin connections play a role of gauge fields and Riemann
curvature tensors correspond to their field strengths. One can then pose an
interesting question: What is the Einstein equations from the gauge theory
point of view? Or equivalently, what is the gauge theory object corresponding
to Einstein manifolds? We show that the Einstein equations in four dimensions
are precisely self-duality equations in Yang-Mills gauge theory and so Einstein
manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R
gauge theory. Specifically, we prove that any Einstein manifold with or without
a cosmological constant always arises as the sum of SU(2)_L instantons and
SU(2)_R anti-instantons. This result explains why an Einstein manifold must be
stable because two kinds of instantons belong to different gauge groups,
instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay
into a vacuum. We further illuminate the stability of Einstein manifolds by
showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.
A Labelling Scheme for Higher Dimensional Simplex Equations
We present a succinct way of obtaining all possible higher dimensional
generalization of Quantum Yang-Baxter Equation (QYBE). Using the scheme, we
could generate the two popular three-simplex equations, namely: Zamolodchikov's
tetrahedron equation (ZTE) and Frenkel and Moore equation (FME).Comment: To appear as a Letter to the Editor in J. Phys. A:Math and Ge
Incompressible strips in dissipative Hall bars as origin of quantized Hall plateaus
We study the current and charge distribution in a two dimensional electron
system, under the conditions of the integer quantized Hall effect, on the basis
of a quasi-local transport model, that includes non-linear screening effects on
the conductivity via the self-consistently calculated density profile. The
existence of ``incompressible strips'' with integer Landau level filling factor
is investigated within a Hartree-type approximation, and non-local effects on
the conductivity along those strips are simulated by a suitable averaging
procedure. This allows us to calculate the Hall and the longitudinal resistance
as continuous functions of the magnetic field B, with plateaus of finite widths
and the well-known, exactly quantized values. We emphasize the close relation
between these plateaus and the existence of incompressible strips, and we show
that for B values within these plateaus the potential variation across the Hall
bar is very different from that for B values between adjacent plateaus, in
agreement with recent experiments.Comment: 13 pages, 11 figures, All color onlin
The Normal State Resistivity of Grain Boundaries in YBa2Cu3O7-delta
Using an optimized bridge geometry we have been able to make accurate
measurements of the properties of YBa2Cu3O7-delta grain boundaries above Tc.
The results show a strong dependence of the change of resistance with
temperature on grain boundary angle. Analysis of our results in the context of
band-bending allows us to estimate the height of the potential barrier present
at the grain boundary interface.Comment: 11 pages, 3 figure
Isolated and non-isolated dwarfs in terms of modified Newtonian dynamics
Within the framework of modified Newtonian dynamics (MOND) we investigate the
kinematics of two dwarf spiral galaxies belonging to very different
environments, namely KK 246 in the Local Void and Holmberg II in the M81 group.
A mass model of the rotation curve of KK 246 is presented for the first time,
and we show that its observed kinematics are consistent with MOND. We re-derive
the outer rotation curve of Holmberg II, by modelling its HI data cube, and
find that its inclination should be closer to face-on than previously derived.
This implies that Holmberg II has a higher rotation velocity in its outer
parts, which, although not very precisely constrained, is consistent with the
MOND prediction.Comment: Accepted in A&A as a Research Note. 6 pages, 3 figure
Synchronization transition of heterogeneously coupled oscillators on scale-free networks
We investigate the synchronization transition of the modified Kuramoto model
where the oscillators form a scale-free network with degree exponent .
An oscillator of degree is coupled to its neighboring oscillators with
asymmetric and degree-dependent coupling in the form of \couplingcoeff
k_i^{\eta-1}. By invoking the mean-field approach, we determine the
synchronization transition point , which is zero (finite) when (). We find eight different synchronization
transition behaviors depending on the values of and , and
derive the critical exponents associated with the order parameter and the
finite-size scaling in each case. The synchronization transition is also
studied from the perspective of cluster formation of synchronized vertices. The
cluster-size distribution and the largest cluster size as a function of the
system size are derived for each case using the generating function technique.
Our analytic results are confirmed by numerical simulations.Comment: 11 pages, 3 figures and two table
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