7,087 research outputs found
On the topology of conformally compact Einstein 4-manifolds
In this paper we study the topology of conformally compact Einstein
4-manifolds. When the conformal infinity has positive Yamabe invariant and the
renormalized volume is also positive we show that the conformally compact
Einstein 4-manifold will have at most finite fundamental group. Under the
further assumption that the renormalized volume is relatively large, we
conclude that the conformally compact Einstein 4-manifold is diffeomorphic to
and its conformal infinity is diffeomorphic to .Comment: 16 page
Chiral anomaly and anomalous finite-size conductivity in graphene
Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host
two pairs of massless two-dimensional Dirac fermions in the absence of or with
negligible spin-orbit coupling. It is known that the existence of non-zero
electric polarization in reduced momentum space which is associated with a
hidden chiral symmetry will lead to the zero-energy flat band of zigzag
nanoribbon. The Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral
charges at different valleys can be realized in a confined ribbon of finite
width. In the laterally diffusive regime, the finite-size correction to
conductivity is always positive and goes inversely with the square of the
lateral dimension W, which is different from the finite-size correction
inversely with W from boundary modes. This anomalous finite-size conductivity
reveals the signature of the chiral anomaly in graphene, and is measurable
experimentally.Comment: 5 pages, 2 figure
Some Progress in Conformal Geometry
This is a survey paper of our current research on the theory of partial
differential equations in conformal geometry. Our intention is to describe some
of our current works in a rather brief and expository fashion. We are not
giving a comprehensive survey on the subject and references cited here are not
intended to be complete. We introduce a bubble tree structure to study the
degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying
some global conformal bounds on compact manifolds of dimension 4. As
applications, we establish a gap theorem, a finiteness theorem for
diffeomorphism type for this class, and diameter bound of the
-metrics in a class of conformal 4-manifolds. For conformally compact
Einstein metrics we introduce an eigenfunction compactification. As a
consequence we obtain some topological constraints in terms of renormalized
volumes.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
Single hole motion in LaMnO
We study single hole motion in LaMnO using the classical approximation
for JT lattice distortions, a modified Lang-Firsov approximation for dynamical
breathing-mode phonons, and the self-consistent Born approximation (verified by
exact diagonalization) for hole-orbital-excitation scattering. We show that in
the realistic parameter space for LaMnO, quantum effects of electron-phonon
interaction are small. The quasiparticle bandwidth in the
purely orbital t-J model. It is strikingly broadened to be of order by
strong static Jahn-Teller lattice distortions even when the polaronic band
narrowing is taken into account.Comment: 4 pages, 4 eps figure
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