Large tunable valley splitting in edge-free graphene quantum dots on boron nitride

Coherent manipulation of binary degrees of freedom is at the heart of modern quantum technologies. Graphene offers two binary degrees: the electron spin and the valley. Efficient spin control has been demonstrated in many solid state systems, while exploitation of the valley has only recently been started, yet without control on the single electron level. Here, we show that van-der Waals stacking of graphene onto hexagonal boron nitride offers a natural platform for valley control. We use a graphene quantum dot induced by the tip of a scanning tunneling microscope and demonstrate valley splitting that is tunable from -5 to +10 meV (including valley inversion) by sub-10-nm displacements of the quantum dot position. This boosts the range of controlled valley splitting by about one order of magnitude. The tunable inversion of spin and valley states should enable coherent superposition of these degrees of freedom as a first step towards graphene-based qubits

Nontrivial Dynamics in the Early Stages of Inflation

Inflationary cosmologies, regarded as dynamical systems, have rather simple asymptotic behavior, insofar as the cosmic baldness principle holds. Nevertheless, in the early stages of an inflationary process, the dynamical behavior may be very complex. In this paper, we show how even a simple inflationary scenario, based on Linde's ``chaotic inflation'' proposal, manifests nontrivial dynamical effects such as the breakup of invariant tori, formation of cantori and Arnol'd's diffusion. The relevance of such effects is highlighted by the fact that even the occurrence or not of inflation in a given Universe is dependent upon them.Comment: 26 pages, Latex, 9 Figures available on request, GTCRG-94-1

Conserved CDC20 Cell Cycle Functions Are Carried out by Two of the Five Isoforms in Arabidopsis thaliana

The CDC20 and Cdh1/CCS52 proteins are substrate determinants and activators of the Anaphase Promoting Complex/Cyclosome (APC/C) E3 ubiquitin ligase and as such they control the mitotic cell cycle by targeting the degradation of various cell cycle regulators. In yeasts and animals the main CDC20 function is the destruction of securin and mitotic cyclins. Plants have multiple CDC20 gene copies whose functions have not been explored yet. In Arabidopsis thaliana there are five CDC20 isoforms and here we aimed at defining their contribution to cell cycle regulation, substrate selectivity and plant development.Studying the gene structure and phylogeny of plant CDC20s, the expression of the five AtCDC20 gene copies and their interactions with the APC/C subunit APC10, the CCS52 proteins, components of the mitotic checkpoint complex (MCC) and mitotic cyclin substrates, conserved CDC20 functions could be assigned for AtCDC20.1 and AtCDC20.2. The other three intron-less genes were silent and specific for Arabidopsis. We show that AtCDC20.1 and AtCDC20.2 are components of the MCC and interact with mitotic cyclins with unexpected specificity. AtCDC20.1 and AtCDC20.2 are expressed in meristems, organ primordia and AtCDC20.1 also in pollen grains and developing seeds. Knocking down both genes simultaneously by RNAi resulted in severe delay in plant development and male sterility. In these lines, the meristem size was reduced while the cell size and ploidy levels were unaffected indicating that the lower cell number and likely slowdown of the cell cycle are the cause of reduced plant growth.The intron-containing CDC20 gene copies provide conserved and redundant functions for cell cycle progression in plants and are required for meristem maintenance, plant growth and male gametophyte formation. The Arabidopsis-specific intron-less genes are possibly "retrogenes" and have hitherto undefined functions or are pseudogenes

Resonances in a chaotic attractor crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle--Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises

On the Integrability of Intermediate Distributions for Anosov Diffeomorphisms

. We study the integrability of intermediate distributions for Anosov diffeomorphisms and provide an example of C 1 \GammaAnosov diffeomorphism on three dimensional torus whose intermediate stable foliation has leaves that admit only a finite number of derivatives. We also show that this phenomenon is quite abundant. In dimension four or higher this can happen even if the Lyapunov exponents at periodic orbits are constant. 1. Introduction Let F be a C r \Gammadiffeomorphism of a compact smooth Riemannian manifold M , r = 1; 2; \Delta \Delta \Delta ; 1 and \Gamma 0 (TM) the space of C 0 \Gammavector fields on M . The map F induces an invertible bounded linear operator on \Gamma 0 (TM) by: F v(x) = DFv(F \Gamma1 (x)); v(x) 2 \Gamma 0 (TM); x 2 M: The Mather spectrum oe(F ) is defined to be the spectrum of the complexification of F . In [M], Mather showed that F is an Anosov system, if and only if 1 = 2 oe(F ), and moreover, if the nonperiodic points of F are dense in M ..