Itinerant Ferromagnetism in the electronic localization limit

We present Hall effect, $R_{xy}(H)$, and magnetoresistance, $R_{xx}(H)$, measurements of ultrathin films of Ni, Co and Fe with thicknesses varying between 0.2-8 nm and resistances between 1 M$\Omega$ - 100 $\Omega.$ Both measurements show that films having resistance above a critical value, $R_{C}$, (thickness below a critical value, $d_{C}$) show no signs for ferromagnetism. Ferromagnetism appears only for films with $R<R_{C}$, where $R_{C}$ is material dependent. We raise the possibility that the reason for the absence of spontaneous magnetization is suppression of itinerant ferromagnetism by electronic disorder in the strong localization regime.Comment: 4 pages, 4 figure

How Far Has Africa Come in Reducing its Anti-agricultural Policy Bias?

For decades, earnings from farming in many African countries have been depressed by own-country policies such as export restrictions on cash crop products, as well as by governments of richer countries favoring their farmers with import barriers and subsidies. Both sets of policies have reduced national and global economic welfare, inhibited agricultural trade and economic growth, and may well have added to income inequality and poverty in Africa. During the past two decades, however, numerous African country governments have reduced their sectoral and trade policy distortions, while some high-income countries also have begun reducing market-distorting aspects of their farm policies. This paper provides new estimates of the changing extent of policy distortions to prices faced by African farmers over the past half century. It compares that pattern with similar estimates from Asia and Latin America, before discussing prospects for further pro-poor policy reform of agricultural price and trade policies.distorted incentives, export taxes in Africa, agricultural and trade policy reforms

Absence of weak antilocalization in ferromagnetic films

We present magnetoresistance measurements performed on ultrathin films of amorphous Ni and Fe. In these films the Curie temperature drops to zero at small thickness, making it possible to study the effect of ferromagnetism on localization. We find that non-ferromagnetic films are characterized by positive magnetoresistance. This is interpreted as resulting from weak antilocalization due to strong Bychkov-Rashba spin orbit scattering. As the films become ferromagnetic the magnetoresistance changes sign and becomes negative. We analyze our data to identify the individual contributions of weak localization, weak antilocalization and anisotropic magnetoresistance and conclude that the magnetic order suppresses the influence of spin-orbit effects on localization phenomena in agreement with theoretical predictions.Comment: 6 pages, 6 figure

Recurrence to shrinking targets on typical self-affine fractals

We explore the problem of finding the Hausdorff dimension of the set of points that recur to shrinking targets on a self-affine fractal. To be exact, we study the dimension of a certain related symbolic recurrence set. In many cases this set is equivalent to the recurring set on the fractal

Adapting approximate memory potentials for time-dependent density functional theory

Frequency dependent exchange correlation kernels for time-dependent density functional theory can be used to construct approximate exchange-correlation potentials. The resulting potentials are usually not translationally covariant nor do they obey the so-called zero-force condition. These two basic symme-try requirements are essential for using the potentials in actual applications (even within the linear re-sponse regime). We provide two pragmatic methods for imposing these conditions. As an example we take the Gross and Kohn (GK) frequency dependent XC functional (Phys. Rev.Lett. 55, 2850 (1985)), correct it, and numerically test it on a sodium metal cluster. Violation of the basic symme-tries causes instabilities or spurious low frequency modes

Yang-Mills theory over surfaces and the Atiyah-Segal theorem

In this paper we explain how Morse theory for the Yang-Mills functional can be used to prove an analogue, for surface groups, of the Atiyah-Segal theorem. Classically, the Atiyah-Segal theorem relates the representation ring R(\Gamma) of a compact Lie group $\Gamma$ to the complex K-theory of the classifying space $B\Gamma$. For infinite discrete groups, it is necessary to take into account deformations of representations, and with this in mind we replace the representation ring by Carlsson's deformation $K$--theory spectrum \K (\Gamma) (the homotopy-theoretical analogue of $R(\Gamma)$). Our main theorem provides an isomorphism in homotopy \K_*(\pi_1 \Sigma)\isom K^{-*}(\Sigma) for all compact, aspherical surfaces $\Sigma$ and all $*>0$. Combining this result with work of Tyler Lawson, we obtain homotopy theoretical information about the stable moduli space of flat unitary connections over surfaces.Comment: 43 pages. Changes in v4: improved results in Section 7, simplified arguments in the Appendix, various minor revision

Webs of Lagrangian Tori in Projective Symplectic Manifolds

For a Lagrangian torus A in a simply-connected projective symplectic manifold M, we prove that M has a hypersurface disjoint from a deformation of A. This implies that a Lagrangian torus in a compact hyperk\"ahler manifold is a fiber of an almost holomorphic Lagrangian fibration, giving an affirmative answer to a question of Beauville's. Our proof employs two different tools: the theory of action-angle variables for algebraically completely integrable Hamiltonian systems and Wielandt's theory of subnormal subgroups.Comment: 18 pages, minor latex problem fixe

Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

Friction of the surface plasmon by high-energy particle-hole pairs: Are memory effects important?

We show that the dynamics of the surface plasmon in metallic nanoparticles damped by its interaction with particle-hole excitations can be modelled by a single degree of freedom coupled to an environment. In this approach, the fast decrease of the dipole matrix elements that couple the plasmon to particle-hole pairs with the energy of the excitation allows a separation of the Hilbert space into low- and high-energy subspaces at a characteristic energy that we estimate. A picture of the spectrum consisting of a collective excitation built from low-energy excitations which interacts with high-energy particle-hole states can be formalised. The high-energy excitations yield an approximate description of a dissipative environment (or "bath") within a finite confined system. Estimates for the relevant timescales establish the Markovian character of the bath dynamics with respect to the surface plasmon evolution for nanoparticles with a radius larger than about 1 nm.Comment: 8 pages, 1 figure; see also cond-mat/070372

Quantum memory effects on the dynamics of electrons in small gold clusters

Electron dynamics in metallic clusters are examined using a time-dependent density functional theory that includes a 'memory term', i.e. attempts to describe temporal non-local correlations. Using the Iwamoto, Gross and Kohn exchange-correlation (XC) kernel we construct a translationally invariant memory action from which an XC potential is derived that is translationally covariant and exerts zero net force on the electrons. An efficient and stable numerical method to solve the resulting Kohn-Sham equations is presented. Using this framework, we study memory effects on electron dynamics in spherical Jellium 'gold clusters'. We find memory significantly broadens the surface plasmon absorption line, yet considerably less than measured in real gold clusters, attributed to the inadequacy of the Jellium model. Two-dimensional pump-probe spectroscopy is used to study the temporal decay profile of the plasmon, finding a fast decay followed by slower tail. Finally, we examine memory effects on high harmonic generation, finding memory narrows emission lines