672,345 research outputs found
Painlev\'e V and time dependent Jacobi polynomials
In this paper we study the simplest deformation on a sequence of orthogonal
polynomials, namely, replacing the original (or reference) weight
defined on an interval by It is a well-known fact that under
such a deformation the recurrence coefficients denoted as and
evolve in according to the Toda equations, giving rise to the
time dependent orthogonal polynomials, using Sogo's terminology. The resulting
"time-dependent" Jacobi polynomials satisfy a linear second order ode. We will
show that the coefficients of this ode are intimately related to a particular
Painlev\'e V. In addition, we show that the coefficient of of the
monic orthogonal polynomials associated with the "time-dependent" Jacobi
weight, satisfies, up to a translation in the Jimbo-Miwa -form of
the same while a recurrence coefficient is up to a
translation in and a linear fractional transformation
These results are found
from combining a pair of non-linear difference equations and a pair of Toda
equations. This will in turn allow us to show that a certain Fredholm
determinant related to a class of Toeplitz plus Hankel operators has a
connection to a Painlev\'e equation
Valley Dependent Optoelectronics from Inversion Symmetry Breaking
Inversion symmetry breaking allows contrasted circular dichroism in different
k-space regions, which takes the extreme form of optical selection rules for
interband transitions at high symmetry points. In materials where band-edges
occur at noncentral valleys, this enables valley dependent interplay of
electrons with light of different circular polarizations, in analogy to spin
dependent optical activities in semiconductors. This discovery is in perfect
harmony with the previous finding of valley contrasted Bloch band features of
orbital magnetic moment and Berry curvatures from inversion symmetry breaking
[Phys. Rev. Lett. 99, 236809 (2007)]. A universal connection is revealed
between the k-resolved optical oscillator strength of interband transitions,
the orbital magnetic moment and the Berry curvatures, which also provides a
principle for optical measurement of orbital magnetization and intrinsic
anomalous Hall conductivity in ferromagnetic systems. The general physics is
demonstrated in graphene where inversion symmetry breaking leads to valley
contrasted optical selection rule for interband transitions. We discuss
graphene based valley optoelectronics applications where light polarization
information can be interconverted with electronic information.Comment: Expanded version, to appear in Phys. Rev.
Spin-Dependent Antenna Splitting Functions
We consider parton showers based on radiation from QCD dipoles or `antennae'.
These showers are built from 2->3 parton splitting processes. The question then
arises of what functions replace the Altarelli-Parisi splitting functions in
this approach. We give a detailed answer to this question, applicable to
antenna showers in which partons carry definite helicity, and to both initial-
and final-state emissions.Comment: 31 pages, 12 figure
A type system for components
In modern distributed systems, dynamic reconfiguration, i.e.,
changing at runtime the communication pattern of a program, is chal-
lenging. Generally, it is difficult to guarantee that such modifications will
not disrupt ongoing computations. In a previous paper, a solution to this
problem was proposed by extending the object-oriented language ABS
with a component model allowing the programmer to: i) perform up-
dates on objects by means of communication ports and their rebinding;
and ii) precisely specify when such updates can safely occur in an object
by means of critical sections. However, improper rebind operations could
still occur and lead to runtime errors. The present paper introduces a
type system for this component model that extends the ABS type system
with the notion of ports and a precise analysis that statically enforces
that no object will attempt illegal rebinding
Electrically driven magnetism on a Pd thin film
Using first-principles density functional calculations we demonstrate that
ferromagnetism can be induced and modulated on an otherwise paramagnetic Pd
metal thin-film surface through application of an external electric field. As
free charges are either accumulated or depleted at the Pd surface to screen the
applied electric field there is a corresponding change in the surface density
of states. This change can be made sufficient for the Fermi-level density of
states to satisfy the Stoner criterion, driving a transition locally at the
surface from a paramagnetic state to an itinerant ferromagnetic state above a
critical applied electric field, Ec. Furthermore, due to the second-order
nature of this transition, the surface magnetization of the ferromagnetic state
just above the transition exhibits a substantial dependence on electric field,
as the result of an enhanced magnetoelectric susceptibility. Using a linearized
Stoner model we explain the occurrence of the itinerant ferromagnetism and
demonstrate that the magnetic moment on the Pd surface follows a square-root
variation with electric field consistent with our first-principles
calculations.Comment: 8 pages, 7 figure
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