72,750 research outputs found
Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions
We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain RN,At=2A−A+,x, t>0, ||t=−||+Ardx, t>0 with the Robin boundary condition +aAA=0, x, where aA>0, the reaction rates (p,q,r,s) satisfy 1<p<()+, q>0, r>0, s0, 1<<+, the diffusion constant is chosen such that 1, and the time relaxation constant is such that 0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 1<p<1+4/N or if r=p+1 and 1<p<, then for aA>1 and sufficiently small the interior spike is stable. (ii) For N=1 if r=2 and 1<p3 or if r=p+1 and 1<p<, then for 0<aA<1 the near-boundary spike is stable. (iii) For N=1 if 3<p<5 and r=2, then there exist a0(0,1) and µ0>1 such that for a(a0,1) and µ=2q/(s+1)(p−1)(1,µ0) the near-boundary spike solution is unstable. This instability is not present for the Neumann boundary condition but only arises for the Robin boundary condition. Furthermore, we show that the corresponding eigenvalue is of order O(1) as 0. ©2007 American Institute of Physic
Valley-kink in Bilayer Graphene at : A Charge Density Signature for Quantum Hall Ferromagnetism
We investigate interaction-induced valley domain walls in bilayer graphene in
the quantum Hall state, subject to a perpendicular electric field that
is antisymmetric across a line in the sample. Such a state can be realized in a
double-gated suspended sample, where the electric field changes sign across a
line in the middle. The non-interacting energy spectrum of the ground state is
characterized by a sharp domain wall between two valley-polarized regions.
Using the Hartree-Fock approximation, we find that the Coulomb interaction
opens a gap between the two lowest-lying states near the Fermi level, yielding
a smooth domain wall with a kink configuration in the valley index. Our results
suggest the possibility to visualize the domain wall via measuring the charge
density difference between the two graphene layers, which we find exhibits a
characteristic pattern. The width of the kink and the resulting pattern can be
tuned by the interplay between the magnetic field and gate electric fields
Interplay between Order and Disorder in the High Performance of Amorphous Transparent Conducting Oxides
Electronic Interface Reconstruction at Polar-Nonpolar Mott Insulator Heterojunctions
We report on a theoretical study of the electronic interface reconstruction
(EIR) induced by polarity discontinuity at a heterojunction between a polar and
a nonpolar Mott insulators, and of the two-dimensional strongly-correlated
electron systems (2DSCESs) which accompany the reconstruction. We derive an
expression for the minimum number of polar layers required to drive the EIR,
and discuss key parameters of the heterojunction system which control 2DSCES
properties. The role of strong correlations in enhancing confinement at the
interface is emphasized.Comment: 7 pages, 6 figures, some typos correcte
The ordered K-theory of a full extension
Let A be a C*-algebra with real rank zero which has the stable weak
cancellation property. Let I be an ideal of A such that I is stable and
satisfies the corona factorization property. We prove that 0->I->A->A/I->0 is a
full extension if and only if the extension is stenotic and K-lexicographic. As
an immediate application, we extend the classification result for graph
C*-algebras obtained by Tomforde and the first named author to the general
non-unital case. In combination with recent results by Katsura, Tomforde, West
and the first author, our result may also be used to give a purely
K-theoretical description of when an essential extension of two simple and
stable graph C*-algebras is again a graph C*-algebra.Comment: Version IV: No changes to the text. We only report that Theorem 4.9
is not correct as stated. See arXiv:1505.05951 for more details. Since
Theorem 4.9 is an application to the main results of the paper, the main
results of this paper are not affected by the error. Version III comments:
Some typos and errors corrected. Some references adde
Relative entropy of entanglement for certain multipartite mixed states
We prove conjectures on the relative entropy of entanglement (REE) for two
families of multipartite qubit states. Thus, analytic expressions of REE for
these families of states can be given. The first family of states are composed
of mixture of some permutation-invariant multi-qubit states. The results
generalized to multi-qudit states are also shown to hold. The second family of
states contain D\"ur's bound entangled states. Along the way, we have discussed
the relation of REE to two other measures: robustness of entanglement and
geometric measure of entanglement, slightly extending previous results.Comment: Single column, 22 pages, 9 figures, comments welcom
Probing the plateau-insulator quantum phase transition in the quantum Hall regime
We report quantum Hall experiments on the plateau-insulator transition in a
low mobility In_{.53} Ga_{.47} As/InP heterostructure. The data for the
longitudinal resistance \rho_{xx} follow an exponential law and we extract a
critical exponent \kappa= .55 \pm .05 which is slightly different from the
established value \kappa = .42 \pm .04 for the plateau transitions. Upon
correction for inhomogeneity effects, which cause the critical conductance
\sigma_{xx}^* to depend marginally on temperature, our data indicate that the
plateau-plateau and plateau- insulator transitions are in the same universality
class.Comment: 4 pages, 4 figures (.eps
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