56,239 research outputs found
Centers and Azumaya loci of finite -algebras
In this paper, we study the center of the finite -algebra
associated with a semi-simple Lie algebra
over an algebraically closed field \mathds{k} of
characteristic , and an arbitrarily given nilpotent element
. We obtain an analogue of Veldkamp's theorem on the center.
For the maximal spectrum , we show that its Azumaya locus
coincides with its smooth locus of smooth points. The former locus reflects
irreducible representations of maximal dimension for
.Comment: 31 page
On the dynamics of a family of renormalization transformations
We study the family of renormalization transformations of the generalized
--dimensional diamond hierarchical Potts model in statistical mechanic and
prove that their Julia sets and non-escaping loci are always connected, where
. In particular, we prove that their Julia sets can never be a
Sierpi\'{n}ski carpet if the parameter is real. We show that the Julia set is a
quasicircle if and only if the parameter lies in the unbounded capture domain
of these models. Moreover, the asymptotic formula of the Hausdorff dimension of
the Julia set is calculated as the parameter tends to infinity.Comment: 21 pages, 5 figures, to appear in J. Math. Anal. App
Vortex-state-mediated Josephson effect
The Josephson effect is a kind of macroscopic quantum phenomenon that
supercurrent flows through a Josephson junction without any voltage applied. We
predict a novel vortex-state-mediated Josephson effect in an SNS Josephson
junction supporting vortices. The vortex-state-mediated supercurrent is
enhanced or reduced significantly in magnitude depending on the junction
length, and exhibits several steps with the number of effective propagating
channels in current-phase evolution at zero temperature. At finite
temperatures, these supercurrent steps persist in the short junction limit, and
develop into sawtooth oscillations if the junction length becomes comparable to
the coherence length of the superconductor, and in later
case a supercurrent reversal can be observed. These findings may provide a
smoking-gun signature of vortex bound states in superconductors and promise
possible applications in future Josephson devices.Comment: 8 pages, 4 figure
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