Jensen-Feynman approach to the statistics of interacting electrons

Faussurier et al. [Phys. Rev. E 65, 016403 (2001)] proposed to use a variational principle relying on Jensen-Feynman (or Gibbs-Bogoliubov) inequality in order to optimize the accounting for two-particle interactions in the calculation of canonical partition functions. It consists in a decomposition into a reference electron system and a first-order correction. The procedure appears to be very efficient in order to evaluate the free energy and the orbital populations. In this work, we present numerical applications of the method and propose to extend it using a reference energy which includes the interaction between two electrons inside a given orbital. This is possible thanks to our efficient recursion relation for the calculation of partition functions. We also show that a linear reference energy, however, is usually sufficient to achieve a good precision and that the most promising way to improve the approach of Faussurier et al. is to apply Jensen's inequality to a more convenient convex function.Comment: submitted to Physical Review

Democratization under the threat of revolution: Evidence from the great reform act of 1832

We examine the link between the threat of violence and democratization in the context of the Great Reform Act passed by the British Parliament in 1832. We geo-reference the so-called Swing riots, which occurred between the 1830 and 1831 parliamentary elections, and compute the number of these riots that happened within a 10 km radius of the 244 English constituencies. Our empirical analysis relates this constituency-specific measure of the threat perceptions held by the 344,000 voters in the Unreformed Parliament to the share of seats won in each constituency by pro-reform politicians in 1831. We find that the Swing riots induced voters to vote for pro-reform politicians after experiencing first-hand the violence of the riots.Toke Aidt thanks the Institute for Quantitative Social Science at Harvard University for the hospitality during the initial stages of this project. Raphaël Franck gratefully acknowledges financial support from the Adar Foundation of the Economics Department at Bar Ilan University. Raphaël Franck wrote part of this paper as Marie Curie Fellow at the Department of Economics at Brown University under funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme (FP 2007-2013) under REA grant agreement PIOF-GA-2012-327760 (TCDOFT). We are also grateful to the Cambridge Group for the History of Population and Social Structure and the ESRC (Grant RES-000-23-1579) for helping us with shape files for the maps of the ancient counties and parishes. We thank Todd Elder and Olmo Silva for sharing their code as well as John Bohstedt and Andrew Reeves for sharing their data with us. The research was supported by the British Academy (grant JHAG097).This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.3982/ECTA1148

Mechanisms for Lasing with Cold Atoms as the Gain Medium

We realize a laser with a cloud of cold rubidium atoms as gain medium, placed in a low-finesse cavity. Three different regimes of laser emission are observed corresponding respectively to Mollow, Raman and Four Wave Mixing mechanisms. We measure an output power of up to 300 $\mu$W and present the main properties of these different lasers in each regime

The actual impedance of non-reflecting boundary conditions : implications for the computation of resonators

Non-reflecting boundary conditions are essential elements in the computation of many compressible flows: such simulations are very sensitive to the treatment of acoustic waves at boundaries. Non-reflecting conditions allow acoustic waves to propagate through boundaries with zero or small levels of reflection into the domain. However, perfectly non-reflecting conditions must be avoided because they can lead to ill-posed problems for the mean flow. Various methods have been proposed to construct boundary conditions which can be sufficiently non-reflecting for the acoustic field while still making the mean-flow problem well posed. This paper analyses a widely-used technique for non-reflecting outlets (Rudy and Strikwerda, Poinsot and Lele). It shows that the correction introduced by these authors can lead to large reflection levels and non-physical resonant behaviors. A simple scaling is proposed to evaluate the relaxation coefficient used in theses methods for a non-reflecting outlet. The proposed scaling is tested for simple cases (ducts) both theoretically and numerically