A concentration inequality for interval maps with an indifferent fixed point

For a map of the unit interval with an indifferent fixed point, we prove an upper bound for the variance of all observables of $n$ variables $K:[0,1]^n\to\R$ which are componentwise Lipschitz. The proof is based on coupling and decay of correlation properties of the map. We then give various applications of this inequality to the almost-sure central limit theorem, the kernel density estimation, the empirical measure and the periodogram.Comment: 26 pages, submitte

A numerical study of infinitely renormalizable area-preserving maps

It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that infinitely renormalizable area-preserving maps admit invariant Cantor sets with a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these Cantor sets for any two infinitely renormalizable maps is conjugated by a transformation that extends to a differentiable function whose derivative is Holder continuous of exponent alpha>0. In this paper we investigate numerically the specific value of alpha. We also present numerical evidence that the normalized derivative cocycle with the base dynamics in the Cantor set is ergodic. Finally, we compute renormalization eigenvalues to a high accuracy to support a conjecture that the renormalization spectrum is real

High-precision abundances of elements in Kepler LEGACY stars. Verification of trends with stellar age

HARPS-N spectra with S/N > 250 and MARCS model atmospheres were used to derive abundances of C, O, Na, Mg, Al, Si, Ca, Ti, Cr, Fe, Ni, Zn, and Y in ten stars from the Kepler LEGACY sample (including the binary pair 16 Cyg A and B) selected to have metallicities in the range -0.15 < [Fe/H] < +0.15 and ages between 1 and 7 Gyr. Stellar gravities were obtained from seismic data and effective temperatures were determined by comparing non-LTE iron abundances derived from FeI and FeII lines. Available non-LTE corrections were also applied when deriving abundances of the other elements. The results support the [X/Fe]-age relations previously found for solar twins. [Mg/Fe], [Al/Fe], and [Zn/Fe] decrease by ~0.1 dex over the lifetime of the Galactic thin disk due to delayed contribution of iron from Type Ia supernovae relative to prompt production of Mg, Al, and Zn in Type II supernovae. [Y/Mg] and [Y/Al], on the other hand, increase by ~0.3 dex, which can be explained by an increasing contribution of s-process elements from low-mass AGB stars as time goes on. The trends of [C/Fe] and [O/Fe] are more complicated due to variations of the ratio between refractory and volatile elements among stars of similar age. Two stars with about the same age as the Sun show very different trends of [X/H] as a function of elemental condensation temperature Tc and for 16 Cyg, the two components have an abundance difference, which increases with Tc. These anomalies may be connected to planet-star interactions.Comment: 13 pages with 7 figures. Accepted for publication in A&

A Numerical Study of the Hierarchical Ising Model: High Temperature Versus Epsilon Expansion

We study numerically the magnetic susceptibility of the hierarchical model with Ising spins ($\sigma =\pm 1$) above the critical temperature and for two values of the epsilon parameter. The integrations are performed exactly, using recursive methods which exploit the symmetries of the model. Lattices with up to $2^18$ sites have been used. Surprisingly, the numerical data can be fitted very well with a simple power law of the form $(1- \beta /\beta _c )^{- \gamma}$for the {\it whole} temperature range. The numerical values for $\gamma$ agree within a few percent with the values calculated with a high-temperature expansion but show significant discrepancies with the epsilon-expansion. We would appreciate comments about these results.Comment: 15 Pages, 12 Figures not included (hard copies available on request), uses phyzzx.te

Dual Fronts Propagating into an Unstable State

The interface between an unstable state and a stable state usually develops a single confined front travelling with constant velocity into the unstable state. Recently, the splitting of such an interface into {\em two} fronts propagating with {\em different} velocities was observed numerically in a magnetic system. The intermediate state is unstable and grows linearly in time. We first establish rigorously the existence of this phenomenon, called ``dual front,'' for a class of structurally unstable one-component models. Then we use this insight to explain dual fronts for a generic two-component reaction-diffusion system, and for the magnetic system.Comment: 19 pages, Postscript, A

New Abundances for Old Stars - Atomic Diffusion at Work in NGC 6397

A homogeneous spectroscopic analysis of unevolved and evolved stars in the metal-poor globular cluster NGC 6397 with FLAMES-UVES reveals systematic trends of stellar surface abundances that are likely caused by atomic diffusion. This finding helps to understand, among other issues, why the lithium abundances of old halo stars are significantly lower than the abundance found to be produced shortly after the Big Bang.Comment: 8 pages, 7 colour figures, 1 table; can also be downloaded via http://www.eso.org/messenger

A Two-Parameter Recursion Formula For Scalar Field Theory

We present a two-parameter family of recursion formulas for scalar field theory. The first parameter is the dimension $(D)$. The second parameter ($\zeta$) allows one to continuously extrapolate between Wilson's approximate recursion formula and the recursion formula of Dyson's hierarchical model. We show numerically that at fixed $D$, the critical exponent $\gamma$ depends continuously on $\zeta$. We suggest the use of the $\zeta -$independence as a guide to construct improved recursion formulas.Comment: 7 pages, uses Revtex, one Postcript figur

Analytical model of non-Markovian decoherence in donor-based charge quantum bits

We develop an analytical model for describing the dynamics of a donor-based charge quantum bit (qubit). As a result, the quantum decoherence of the qubit is analytically obtained and shown to reveal non-Markovian features: The decoherence rate varies with time and even attains negative values, generating a non-exponential decay of the electronic coherence and a later recoherence. The resulting coherence time is inversely proportional to the temperature, thus leading to low decoherence below a material dependent characteristic temperature.Comment: 19 pages, 3 figure