Regularity and decay of solutions of nonlinear harmonic oscillators

We prove sharp analytic regularity and decay at infinity of solutions of variable coefficients nonlinear harmonic oscillators. Namely, we show holomorphic extension to a sector in the complex domain, with a corresponding Gaussian decay, according to the basic properties of the Hermite functions in R^d. Our results apply, in particular, to nonlinear eigenvalue problems for the harmonic oscillator associated to a real-analytic scattering, or asymptotically conic, metric in R^d, as well as to certain perturbations of the classical harmonic oscillator.Comment: 36 page

On the Phase Transition of Conformal Field Theories with Holographic Duals

We study the thermodynamic relations of conformal field theories (CFTs), which are holographically dual to anti-de Sitter-Schwarzschild bulk space-times. A Cardy-Verlinde formula is derived thermodynamically for CFTs living on S^n x R with S^n having an arbitrary radius. The Hawking-Page phase transition of the CFT is described using Landau's theory of phase transitions, and an alternative derivation of the Cardy-Verlinde formula is presented. The condensate in the high temperature phase is identified as being composed of radiational matter.Comment: 10 pages, final version to appear on PL

Pointwise decay and smoothness for semilinear elliptic equations and travelling waves

We derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier multipliers with finitely smooth symbols at the origin. Applications concern the decay and smoothness of travelling waves for nonlinear evolution equations in fluid dynamics and plasma physics

Sharp decay estimates and smoothness for solutions to nonlocal semilinear equations

We consider semilinear equations of the form p(D)u=F(u), with a locally bounded nonlinearity F(u), and a linear part p(D) given by a Fourier multiplier. The multiplier p(\xi) is the sum of positively homogeneous terms, with at least one of them non smooth. This general class of equations includes most physical models for traveling waves in hydrodynamics, the Benjamin-Ono equation being a basic example. We prove sharp pointwise decay estimates for the solutions to such equations, depending on the degree of the non smooth terms in p(\xi). When the nonlinearity is smooth we prove similar estimates for the derivatives of the solution, as well holomorphic extension to a strip, for analytic nonlinearity

Measuring market and inflation risk premia in France and in Germany

This paper studies the role of inflation in the determination of financial asset prices. We estimate an Intertemporal Capital Asset Pricing Model à la Merton (1973), with inflation as an independent source of risk, for France and Germany. Our study also allows us to evaluate how the different nature of the French and German monetary policies before 1999 as well as the convergence process towards the single currency might have affected the role of inflation in the pricing of financial assets. We find that inflation is a significant explanatory factor for the pricing of stocks and government bonds in the two countries. Moreover, while there seems to be no clear structural break in the impact of inflation on asset prices after Stage Three of Economic and Monetary Union, such an impact has been increasingly similar in the two countries after 1999. JEL Classification: C32, C61, E44, G12business cycles, GARCH-in-Mean, Intertemporal CAPM

The sustainability of China's exchange rate policy and capital account liberalisation.

This paper deals with two related issues: the sustainability of China’s exchange rate regime and the opening up of its capital account. The exchange rate discussion deliberately passes over the issue of the “equilibrium” value of the renminbi and its alleged undervaluation – typically at the heart of the current policy debate – and focuses instead on the domestic costs of the current regime and the potential risks to domestic financial stability in the long run. The paper argues that the renminbi exchange rate should be increasingly determined by market forces and that administrative controls should be progressively relinquished. The exchange rate is obviously linked to well-functioning and efficient capital markets, which require no barriers to capital flows. Thus, exchange rate reform has to be correctly sequenced with reform of the capital account to avoid disruptive capital flows. The paper discusses China’s twin surpluses of the current and capital accounts and attempts to identify the drivers of this “anomalous” external position. The pragmatic strategy pursued by the Chinese authorities in the aftermath of the Asian crisis encouraged FDI inflows and favoured the accumulation of a large stock of foreign exchange reserves. Combined with a relatively weak institutional setting, these factors have been important determinants of the pattern and composition of the country’s capital flows and international investment position. Finally, the paper speculates on the outlook for Chinese capital flows should barriers to capital movements be lifted. It argues that whether China continues to supply capital to the rest of the world or eventually becomes a net borrower in international capital markets – as was the case for most of its recent history – will depend on the evolution of its institutions. JEL Classification: F10, F21, F31, F32, P48.China, exchange rate policy, international investment position, capital account liberalisation, institutions.

Uncovered interest parity at distant horizons: evidence on emerging economies & nonlinearities

This paper tests for uncovered interest parity (UIP) at distant horizons for the US and its main trading partners, including both mature and emerging market economies, also exploring the existence of nonlinearities. At long and medium horizons, it finds support in favour of the standard, linear, specification of UIP for dollar rates vis-à-vis major floating currencies, but not vis-à-vis emerging market currencies. Moreover, the paper finds evidence that, not only yield differentials widen, but that US bond yields do react in anticipation of exchange rate movements, notably when these take place vis-à-vis major floating currencies. Last, the paper detects signs of nonlinearities in UIP at the mediumterm horizon for dollar rates vis-à-vis some of the major floating currencies, albeit surrounded by some uncertainty. JEL Classification: E43, F31, F41distant horizon, emerging economies, Nonlinearities, Uncovered interest parity

Assuming Regge trajectories in holographic QCD: from OPE to Chiral Perturbation Theory

The soft wall model in holographic QCD has Regge trajectories but wrong operator product expansion (OPE) for the two-point vectorial QCD Green function. We modify the dilaton potential to comply OPE. We study also the axial two-point function using the same modified dilaton field and an additional scalar field to address chiral symmetry breaking. OPE is recovered adding a boundary term and low energy chiral parameters, $F_\pi$ and $L_{10}$, are well described analytically by the model in terms of Regge spacing and QCD condensates. The model nicely supports and extends previous theoretical analyses advocating Digamma function to study QCD two-point functions in different momentum regions.Comment: Major changes to improve the presentation of the paper but main results unchanged. Added appendix on Regge progressio

Antisymmetric tensors in holographic approaches to QCD

We study real (massive) antisymmetric tensors of rank two in holographic models of QCD based on the gauge/string duality. Our aim is to understand in detail how the AdS/CFT correspondence describes correlators with tensor currents in QCD. To this end we study a set of bootstrapped correlators with spin-1 vector and tensor currents, imposing matching to QCD at the partonic level. We show that a consistent description of this set of correlators yields a very predictive picture. For instance, it imposes strong constraints on infrared boundary conditions and precludes the introduction of dilatonic backgrounds as a mechanism to achieve linear confinement. Additionally, correlators with tensor currents turn out to be especially sensitive to chiral symmetry breaking, thus offering an ideal testing ground for genuine QCD effects. Several phenomenological consequences are explored, such as the nontrivial interplay between $1^{+-}$ states and conventional $1^{--}$ vector mesons.Comment: 15 pages, 2 figures. Minor changes to match the journal versio