Arabia Saudí en 2004: ¿podrá sobrevivir a la amenaza terrorista?

El presente análisis examina la estructura sociopolítica de Arabia Saudí, al tiempo que intenta evaluar si podrá hacer frente al conjunto de tensiones generadas por el desempleo entre los jóvenes, el llamamiento a la yihad por parte de los extremistas y el deterioro de sus relaciones con EEUU en un momento de incertidumbre en el liderazgo del país. El reino de Arabia Saudí, tan esencial para la economía mundial, no sólo debe hacer frente a la amenaza de los extremistas terroristas, sino también al desempleo entre los jóvenes y a una relación con EEUU en proceso de deterioro. Atrapado entre la necesidad de tomar medidas enérgicas para combatir toda forma de disidencia y la necesidad de abrir la sociedad para llevar el país al siglo XXI, el propio liderazgo saudí se halla en un estado de incertidumbre sobre el futuro, sin saber muy bien si aferrarse a su posición privilegiada, o si adaptarse e introducir alguna fórmula que permita algún tipo de reparto del poder. Enfrentado a tales retos, este año resultará crucial para el régimen saudí. El país requiere cambios, pero éstos deberían realizarse desde dentro, en lugar de serle impuestos por terroristas o por una potencia extranjera

Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations

In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton constributions to the partition function, using the formalism introduced in the first part of the treatise [J. Zinn-Justin and U. D. Jentschura, e-print quant-ph/0501136]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific potential which bears an analogy with the Fokker-Planck equation. The latter potential has the peculiar property that the perturbation series for the ground-state energy vanishes to all orders and is thus formally convergent (the ground-state energy, however, is nonzero and positive). For the potentials (ii), (iii), and (iv), we calculate the perturbative B-function as well as the instanton A-function to fourth order in g. We also consider the double-well potential in detail, and present some higher-order analytic as well as numerical calculations to verify explicitly the related conjectures up to the order of three instantons. Strategies analogous to those outlined here could result in new conjectures for problems where our present understanding is more limited.Comment: 55 pages, LaTeX; refs. to part I preprint update

Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions

We consider specific quantum mechanical model problems for which perturbation theory fails to explain physical properties like the eigenvalue spectrum even qualitatively, even if the asymptotic perturbation series is augmented by resummation prescriptions to "cure" the divergence in large orders of perturbation theory. Generalizations of perturbation theory are necessary which include instanton configurations, characterized by nonanalytic factors exp(-a/g) where a is a constant and g is the coupling. In the case of one-dimensional quantum mechanical potentials with two or more degenerate minima, the energy levels may be represented as an infinite sum of terms each of which involves a certain power of a nonanalytic factor and represents itself an infinite divergent series. We attempt to provide a unified representation of related derivations previously found scattered in the literature. For the considered quantum mechanical problems, we discuss the derivation of the instanton contributions from a semi-classical calculation of the corresponding partition function in the path integral formalism. We also explain the relation with the corresponding WKB expansion of the solutions of the Schroedinger equation, or alternatively of the Fredholm determinant det(H-E) (and some explicit calculations that verify this correspondence). We finally recall how these conjectures naturally emerge from a leading-order summation of multi-instanton contributions to the path integral representation of the partition function. The same strategy could result in new conjectures for problems where our present understanding is more limited.Comment: 66 pages, LaTeX; refs. to part II preprint update

Updating the Phase Diagram of the Gross-Neveu Model in 2+1 Dimensions

The method of optimized perturbation theory (OPT) is used to study the phase diagram of the massless Gross-Neveu model in 2+1 dimensions. In the temperature and chemical potential plane, our results give strong support to the existence of a tricritical point and line of first order phase transition, previously only suspected to exist from extensive lattice Monte Carlo simulations. In addition of presenting these results we discuss how the OPT can be implemented in conjunction with the Landau expansion in order to determine all the relevant critical quantities.Comment: 7 pages, 2 eps figures. Replaced with the version that matches the published one (PLB

Structural and Mechanistic Insights into Fast Lithium-Ion Conduction in Li4SiO4-Li3PO4 Solid Electrolytes.

Solid electrolytes that are chemically stable and have a high ionic conductivity would dramatically enhance the safety and operating lifespan of rechargeable lithium batteries. Here, we apply a multi-technique approach to the Li-ion conducting system (1-z)Li4SiO4-(z)Li3PO4 with the aim of developing a solid electrolyte with enhanced ionic conductivity. Previously unidentified superstructure and immiscibility features in high-purity samples are characterized by X-ray and neutron diffraction across a range of compositions (z = 0.0-1.0). Ionic conductivities from AC impedance measurements and large-scale molecular dynamics (MD) simulations are in good agreement, showing very low values in the parent phases (Li4SiO4 and Li3PO4) but orders of magnitude higher conductivities (10(-3) S/cm at 573 K) in the mixed compositions. The MD simulations reveal new mechanistic insights into the mixed Si/P compositions in which Li-ion conduction occurs through 3D pathways and a cooperative interstitial mechanism; such correlated motion is a key factor in promoting high ionic conductivity. Solid-state (6)Li, (7)Li, and (31)P NMR experiments reveal enhanced local Li-ion dynamics and atomic disorder in the solid solutions, which are correlated to the ionic diffusivity. These unique insights will be valuable in developing strategies to optimize the ionic conductivity in this system and to identify next-generation solid electrolytes.The ALISTORE ERI and CNRS are acknowledged for supporting Y.D. through a joint Ph.D. scholarship between Picardie (France) and Bath (UK). The authors thank D. Sheptyakov (PSI, Switzerland) and M. Bianchini (ILL-Grenoble, France) for assistance with neutron diffraction experiments, and M. T. Dunstan (Cambridge, UK) for assistance with NMR experiments. Financial support from the EPSRC Energy Materials Programme (Grant EP/K016288) is gratefully acknowledged. The HPC Materials Chemistry Consortium (EP/L000202) allowed use of the ARCHER facilities. O.P. and S.E. acknowledge support from a Marie Skłodowska-Curie Fellowship (H2020-MSCA-IF-2014-EF, no. 655444) and an ERASMUS+ scholarship, respectively.This is the author accepted manuscript. The final version is available from the American Chemical Society via http://dx.doi.org/10.1021/jacs.5b0444

Convergent resummed linear delta expansion in the critical O(N) (\phi_i^2)^2_{3d} model

The nonperturbative linear delta expansion (LDE) method is applied to the critical O(N) phi^4 three-dimensional field theory which has been widely used to study the critical temperature of condensation of dilute weakly interacting homogeneous Bose gases. We study the higher order convergence of the LDE as it is usually applied to this problem. We show how to improve both, the large-N and finite N=2, LDE results with an efficient resummation technique which accelerates convergence. In the large N limit, it reproduces the known exact result within numerical integration accuracy. In the finite N=2 case, our improved results support the recent numerical Monte Carlo estimates for the critical transition temperature of Bose-Einstein condensation.Comment: 4 pages, Revtex 4. A misprint in Eq. (3) was corrected and ref. 17 (cond-mat/0207295) update

Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem

We investigate the convergence properties of optimized perturbation theory, or linear $\delta$ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature T_c for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of $T_c$ in the large-N limit, when the relevant effective static action describing the system is extended to O(N) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for $T_c$ already at the first non-trivial order. Next, we consider the finite N=2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.Comment: 38 pages, 3 eps figures, Revtex4. Final version in press Phys. Rev.

Variational Quark Mass Expansion and the Order Parameters of Chiral Symmetry Breaking

We investigate in some detail a "variational mass" expansion approach, generalized from a similar construction developed in the Gross-Neveu model, to evaluate the basic order parameters of the dynamical breaking of the $SU(2)_L \times SU(2)_R$ and $SU(3)_L \times SU(3)_R$ chiral symmetries in QCD. The method starts with a reorganization of the ordinary perturbation theory with the addition of an arbitrary quark mass $m$. The new perturbative series can be summed to all orders thanks to renormalization group properties, with specific boundary conditions, and advocated analytic continuation in $m$ properties. In the approximation where the explicit breakdown of the chiral symmetries due to small current quark masses is neglected, we derive ansatzes for the dynamical contribution to the "constituent" masses $M_q$ of the $u,d,s$ quarks; the pion decay constant $F_\pi$; and the quark condensate $$ in terms of the basic QCD scale $\Lambda_{\bar{MS}}$. Those ansatzes are then optimized, in a sense to be specified, and also explicit symmetry breaking mass terms can be consistently introduced in the framework. The obtained values of $F_\pi$ and $M_q$ are roughly in agreement with what is expected from other non-perturbative methods. In contrast we obtain quite a small value of $|< \bar q q >|$ within our approach. The possible interpretation of the latter results is briefly discussed.Comment: 40 pages, LaTex, 2 PS figures. Additions in section 2.2 to better explain the relation between the current mass and the dynamical mass ansatz. Minor misprints corrected. Version to appear in Phys. Rev.

Herkules – Held zwischen Tugend und Hybris. Ein europäischer Erinnerungsort der Frühen Neuzeit?

This essay traces some of the contexts and media in which "Heracles-Hercules" - as a hero between virtue and hubris - was visible in European societies from the end of the middle ages onwards. It discusses whether this example of the reception, appropriation and transformation of classical myths in the early modern period can be understood as a European "lieu de mémoire", and to what extent the concept of "lieux de mémoire" (or sites of memory) can foster our understanding of a particular object of study (here the Heracles/Hercules myth). Against this backdrop, we conclude with some general questions about the more ambitious project* of a comprehensive register of European "lieux de mémoire". * * Published as: Boer, Pim den / Duchhardt, Heinz / Kreis, Georg / Schmale, Wolfgang (eds.): Europäische Erinnerungsorte, 3 vols., Munich 2011–201

Un essai de mythologie comparée au début du XVIIe siècle

Seznec Jean. Un essai de mythologie comparée au début du XVIIe siècle. In: Mélanges d'archéologie et d'histoire, tome 48, 1931. pp. 268-281