1,004 research outputs found
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
Universal scheme to generate metal-insulator transition in disordered systems
We propose a scheme to generate metal-insulator transition in random binary
layer (RBL) model, which is constructed by randomly assigning two types of
layers. Based on a tight-binding Hamiltonian, the localization length is
calculated for a variety of RBLs with different cross section geometries by
using the transfer-matrix method. Both analytical and numerical results show
that a band of extended states could appear in the RBLs and the systems behave
as metals by properly tuning the model parameters, due to the existence of a
completely ordered subband, leading to a metal-insulator transition in
parameter space. Furthermore, the extended states are irrespective of the
diagonal and off-diagonal disorder strengths. Our results can be generalized to
two- and three-dimensional disordered systems with arbitrary layer structures,
and may be realized in Bose-Einstein condensates.Comment: 5 ages, 4 figure
Identify the topological superconducting order in a multi-band quantum wire
How to distinguish the zero-bias peak (ZBP) caused by the Majorana fermions
from that by the other effects remains a challenge in detecting the topological
order of a quantum wire. In this paper we propose to distinguish the
topological superconducting phase from the topologically trivial phase by
making a Josephson junction of the quantum wire attached to a side lead and
then measuring the tunneling conductance through it as the phase difference
across the junction varies. Even if the ZBPs exist in both phases, we
can identify the topological superconducting phase by a conductance peak at
and a nearby butterfly pattern.Comment: 5 pages, 4 figure
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