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 $w_0(x)$ defined on an interval by $w_0(x)e^{-tx}.$ It is a well-known fact that under such a deformation the recurrence coefficients denoted as $\alpha_n$ and $\beta_n$ evolve in $t$ 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 $z^{n-1}$ of the monic orthogonal polynomials associated with the "time-dependent" Jacobi weight, satisfies, up to a translation in $t,$ the Jimbo-Miwa $\sigma$-form of the same $P_{V};$ while a recurrence coefficient $\alpha_n(t),$ is up to a translation in $t$ and a linear fractional transformation $P_{V}(\alpha^2/2,-\beta^2/2, 2n+1+\alpha+\beta,-1/2).$ 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