Collective synchronization in populations of globally coupled phase oscillators with drifting frequencies

We generalize the Kuramoto model for coupled phase oscillators by allowing the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such drifting frequencies were recently measured in cellular populations of circadian oscillator and inspired our work. Linear stability analysis of the Fokker-Planck equation for an infinite population is amenable to exact solution and we show that the incoherent state is unstable passed a critical coupling strength K_c(\ga, \sigf), where \ga is the inverse characteristic drifting time and \sigf the asymptotic frequency dispersion. Expectedly $K_c$ agrees with the noisy Kuramoto model in the large \ga (Schmolukowski) limit but increases slower as \ga decreases. Asymptotic expansion of the solution for \ga\to 0 shows that the noiseless Kuramoto model with Gaussian frequency distribution is recovered in that limit. Thus varying a single parameter allows to interpolate smoothly between two regimes: one dominated by the frequency dispersion and the other by phase diffusion.Comment: 5 pages, 5 figures, accepted in Phys. Rev.

Reactive Hall response

The zero temperature Hall constant R_H, described by reactive (nondissipative) conductivities, is analyzed within linear response theory. It is found that in a certain limit, R_H is directly related to the density dependence of the Drude weight implying a simple picture for the change of sign of charge carriers in the vicinity of a Mott-Hubbard transition. This novel formulation is applied to the calculation of R_H in quasi-one dimensional and ladder prototype interacting electron systems.Comment: 4 pages, 3 Postscript figure

The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature

Motivated by recent investigations of transport properties of strongly correlated 1d models and thermal conductivity measurements of quasi 1d magnetic systems we present results for the integrable spin-1/2 $XXZ$ chain. The thermal conductivity $\kappa(\omega)$ of this model has $\Re\kappa(\omega)=\tilde\kappa \delta(\omega)$, i.e. it is infinite for zero frequency $\omega$. The weight $\tilde\kappa$ of the delta peak is calculated exactly by a lattice path integral formulation. Numerical results for wide ranges of temperature and anisotropy are presented. The low and high temperature limits are studied analytically.Comment: 12 page

Finite temperature Drude weight of the one dimensional spin 1/2 Heisenberg model}

Using the Bethe ansatz method, the zero frequency contribution (Drude weight) to the spin current correlations is analyzed for the easy plane antiferromagnetic Heisenberg model. The Drude weight is a monotonically decreasing function of temperature for all 0<Delta< 1, it approaches the zero temperature value with a power law and it appears to vanish for all finite temperatures at the isotropic Delta=1 point.Comment: 5 pages, 2 Postscript figure

Low-temperature transport in Heisenberg chains

A technique to determine accurately transport properties of integrable and non-integrable quantum-spin chains at finite temperatures by Quantum Monte-Carlo is presented. The reduction of the Drude weight by interactions in the integrable gapless regime is evaluated. Evidence for the absence of a Drude weight in the gapless regime of a non-integrable system with longer-ranged interactions is presented. We estimate the effect of the non-integrability on the transport properties and compare with recent experiments on one-dimensional quantum-spin chains.Comment: accepted for publication (PRL

An ingress and a complete transit of HD 80606 b

We have used four telescopes at different longitudes to obtain near-continuous lightcurve coverage of the star HD 80606 as it was transited by its \sim 4-MJup planet. The observations were performed during the predicted transit windows around the 25th of October 2008 and the 14th of February 2009. Our data set is unique in that it simultaneously constrains the duration of the transit and the planet's period. Our Markov-Chain Monte Carlo analysis of the light curves, combined with constraints from radial-velocity data, yields system parameters consistent with previously reported values. We find a planet-to-star radius ratio marginally smaller than previously reported, corresponding to a planet radius of Rp = 0.921 \pm 0.036RJup .Comment: 6 pages, 2 figures, MNRAS accepte

Transport and conservation laws

We study the lowest order conservation laws in one-dimensional (1D) integrable quantum many-body models (IQM) as the Heisenberg spin 1/2 chain, the Hubbard and t-J model. We show that the energy current is closely related to the first conservation law in these models and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero frequency component of the conductivity) and so ideal conductivity at finite temperatures.Comment: 6 pages, Late

The CORALIE survey for southern extrasolar planets. XVI. Discovery of a planetary system around HD 147018 and of two long period and massive planets orbiting HD 171238 and HD 204313

We report the detection of a double planetary system around HD 140718 as well as the discovery of two long period and massive planets orbiting HD 171238 and HD 204313. Those discoveries were made with the CORALIE Echelle spectrograph mounted on the 1.2-m Euler Swiss telescope located at La Silla Observatory, Chile. The planetary system orbiting the nearby G9 dwarf HD 147018 is composed of an eccentric inner planet (e=0.47) with twice the mass of Jupiter (2.1 MJup ) and with an orbital period of 44.24 days. The outer planet is even more massive (6.6 MJup) with a slightly eccentric orbit (e=0.13) and a period of 1008 days. The planet orbiting HD 171238 has a minimum mass of 2.6 MJup, a period of 1523 days and an eccentricity of 0.40. It orbits a G8 dwarfs at 2.5 AU. The last planet, HD 204313 b, is a 4.0 MJup -planet with a period of 5.3 years and has a low eccentricity (e = 0.13). It orbits a G5 dwarfs at 3.1 AU. The three parent stars are metal rich, which further strengthened the case that massive planets tend to form around metal rich stars.Comment: 6 pages, 6 figures, accepted for publication in A&

Replica Symmetry Breaking in Attractor Neural Network Models

The phenomenon of replica symmetry breaking is investigated for the retrieval phases of Hopfield-type network models. The basic calculation is done for the generalized version of the standard model introduced by Horner [1] and by Perez-Vicente and Amit [2] which can exhibit low mean levels of neural activity. For a mean activity $\bar a =1/2$ the Hopfield model is recovered. In this case, surprisingly enough, we cannot confirm the well known one step replica symmetry breaking (1RSB) result for the storage capacity which was presented by Crisanti, Amit and Gutfreund [3] (\alpha_c^{\hbox{\mf 1RSB}}\simeq 0.144). Rather, we find that 1RSB- and 2RSB-Ans\"atze yield only slightly increased capacities as compared to the replica symmetric value (\alpha_c^{\hbox{\mf 1RSB}}\simeq 0.138\,186 and \alpha_c^{\hbox{\mf 2RSB}}\simeq 0.138\,187 compared to \alpha_c^{\hbox{\mf RS}}\simeq 0.137\,905), significantly smaller also than the value \alpha_c^{\hbox{\mf sim}} = 0.145\pm 0.009 reported from simulation studies. These values still lie within the recently discovered reentrant phase [4]. We conjecture that in the infinite Parisi-scheme the reentrant behaviour disappears as is the case in the SK-spin-glass model (Parisi--Toulouse-hypothesis). The same qualitative results are obtained in the low activity range.Comment: Latex file, 20 pages, 8 Figures available from the authors upon request, HD-TVP-94-

Diffusive energy transport in the S=1 Haldane chain compound AgVP2S6

We present the results of measurements of the thermal conductivity $\kappa$ of the spin S=1 chain compound AgVP_2S_6 in the temperature range between 2 and 300 K and with the heat flow directed either along or perpendicular to the chain direction. The analysis of the anisotropy of the heat transport allowed for the identification of a small but non-negligible magnon contribution $\kappa_m$ along the chains, superimposed on the dominant phonon contribution $\kappa_ph$. At temperatures above about 100 K the energy diffusion constant D_E(T), calculated from the $\kappa_m(T)$ data, exhibits similar features as the spin diffusion constant D_S(T), previously measured by NMR. In this regime, the behaviour of both transport parameters is consistent with a diffusion process that is caused by interactions inherent to one-dimensional S=1 spin systems.Comment: 6 pages, 4 figure