On the asymptotic expansion of the solutions of the separated nonlinear Schroedinger equation

Nonlinear Schr\"odinger equation (with the Schwarzian initial data) is important in nonlinear optics, Bose condensation and in the theory of strongly correlated electrons. The asymptotic solutions in the region $x/t={\cal O}(1)$, $t\to\infty$, can be represented as a double series in $t^{-1}$ and $\ln t$. Our current purpose is the description of the asymptotics of the coefficients of the series.Comment: 11 pages, LaTe

Quantum and Classical Integrable Systems

The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the universal enveloping algebra of an affine Lie algebra, or its q-deformation.) A similar relation also holds in the classical case. We discuss different guises of this very important relation and its implication for the description of the spectrum and the eigenfunctions of the quantum system. Parallels between the classical and the quantum cases are thoroughly discussed.Comment: 59 pages, LaTeX2.09 with AMS symbols. Lectures at the CIMPA Winter School on Nonlinear Systems, Pondicherry, January 199

Low-temperature electrical transport in bilayer manganite La1.2_{1.2}Sr1.8_{1.8}Mn2_{2}O7_{7}

The temperature $T$ and magnetic field $H$ dependence of anisotropic in-plane $\rho_{ab}$ and out-of-plane $\rho_{c}$ resistivities have been investigated in single crystals of the bilayer manganite La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$. Below the Curie transition temperature $T_c=$ 125 K, $\rho_{ab}$ and $\rho_{c}$ display almost the same temperature dependence with an up-turn around 50 K. In the metallic regime (50 K $\leq T \leq$ 110 K), both $\rho_{ab}(T)$ and $\rho_{c}(T)$ follow a $T^{9/2}$ dependence, consistent with the two-magnon scattering. We found that the value of the proportionality coefficient $B_{ab}^{fit}$ and the ratio of the exchange interaction $J_{ab}/J_c$ obtained by fitting the data are in excellent agreement with the calculated $B_{ab}$ based on the two-magnon model and $J_{ab}/J_c$ deduced from neutron scattering, respectively. This provides further support for this scattering mechanism. At even lower $T$, in the non-metallic regime ($T<$ 50 K), {\it both} the in-plane $\sigma_{ab}$ and out-of-plane $\sigma_{c}$ conductivities obey a $T^{1/2}$ dependence, consistent with weak localization effects. Hence, this demonstrates the three-dimensional metallic nature of the bilayer manganite La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ at $T<T_c$.Comment: 7 pages and 5 figures, accepted for publication in Phys. Rev.

On post-Lie algebras, Lie--Butcher series and moving frames

Pre-Lie (or Vinberg) algebras arise from flat and torsion-free connections on differential manifolds. They have been studied extensively in recent years, both from algebraic operadic points of view and through numerous applications in numerical analysis, control theory, stochastic differential equations and renormalization. Butcher series are formal power series founded on pre-Lie algebras, used in numerical analysis to study geometric properties of flows on euclidean spaces. Motivated by the analysis of flows on manifolds and homogeneous spaces, we investigate algebras arising from flat connections with constant torsion, leading to the definition of post-Lie algebras, a generalization of pre-Lie algebras. Whereas pre-Lie algebras are intimately associated with euclidean geometry, post-Lie algebras occur naturally in the differential geometry of homogeneous spaces, and are also closely related to Cartan's method of moving frames. Lie--Butcher series combine Butcher series with Lie series and are used to analyze flows on manifolds. In this paper we show that Lie--Butcher series are founded on post-Lie algebras. The functorial relations between post-Lie algebras and their enveloping algebras, called D-algebras, are explored. Furthermore, we develop new formulas for computations in free post-Lie algebras and D-algebras, based on recursions in a magma, and we show that Lie--Butcher series are related to invariants of curves described by moving frames.Comment: added discussion of post-Lie algebroid

Evading the CKM Hierarchy: Intrinsic Charm in B Decays

We show that the presence of intrinsic charm in the hadrons' light-cone wave functions, even at a few percent level, provides new, competitive decay mechanisms for B decays which are nominally CKM-suppressed. For example, the weak decays of the B-meson to two-body exclusive states consisting of strange plus light hadrons, such as B\to\pi K, are expected to be dominated by penguin contributions since the tree-level b\to s u\bar u decay is CKM suppressed. However, higher Fock states in the B wave function containing charm quark pairs can mediate the decay via a CKM-favored b\to s c\bar c tree-level transition. Such intrinsic charm contributions can be phenomenologically significant. Since they mimic the amplitude structure of ``charming'' penguin contributions, charming penguins need not be penguins at all.Comment: 28 pages, 6 figures, published version. References added, minor change

Search for Λc+→pK+π−\Lambda_c^+ \to p K^+ \pi^- and Ds+→K+K+π−D_s^+ \to K^+ K^+ \pi^- Using Genetic Programming Event Selection

We apply a genetic programming technique to search for the double Cabibbo suppressed decays $\Lambda_c^+ \to p K^+ \pi^-$ and $D_s^+ \to K^+ K^+ \pi^-$. We normalize these decays to their Cabibbo favored partners and find $\text{BR}($\Lambda_c^+ \to p K^+ \pi^-$)/\text{BR}($\Lambda_c^+ \to p K^- \pi^+$) = (0.05 \pm 0.26 \pm 0.02)$ and $\text{BR}($D_s^+ \to K^+ K^+ \pi^-$)/\text{BR}($D_s^+ \to K^+ K^- \pi^+$) = (0.52\pm 0.17\pm 0.11)$ where the first errors are statistical and the second are systematic. Expressed as 90% confidence levels (CL), we find $< 0.46$ and $< 0.78$ respectively. This is the first successful use of genetic programming in a high energy physics data analysis.Comment: 10 page

A Non-parametric Approach to the D+ to K*0bar mu+ nu Form Factors

Using a large sample of D+ -> K- pi+ mu+ nu decays collected by the FOCUS photoproduction experiment at Fermilab, we present the first measurements of the helicity basis form factors free from the assumption of spectroscopic pole dominance. We also present the first information on the form factor that controls the s-wave interference discussed in a previous paper by the FOCUS collaboration. We find reasonable agreement with the usual assumption of spectroscopic pole dominance and measured form factor ratios.Comment: 14 pages, 5 figures, and 2 tables. We updated the previous version by changing some words, removing one plot, and adding two tables. These changes are mostly stylisti

Dalitz plot analysis of D_s+ and D+ decay to pi+pi-pi+ using the K-matrix formalism

FOCUS results from Dalitz plot analysis of D_s+ and D+ to pi+pi-pi+ are presented. The K-matrix formalism is applied to charm decays for the first time to fully exploit the already existing knowledge coming from the light-meson spectroscopy experiments. In particular all the measured dynamics of the S-wave pipi scattering, characterized by broad/overlapping resonances and large non-resonant background, can be properly included. This paper studies the extent to which the K-matrix approach is able to reproduce the observed Dalitz plot and thus help us to understand the underlying dynamics. The results are discussed, along with their possible implications on the controversial nature of the sigma meson.Comment: To be submitted to Phys.Lett.B A misprint corrected in formula

Measurement of the branching ratio of the decay D^0 -> \pi^-\mu^+\nu relative to D^0 -> K^-\mu^+\nu

We present a new measurement of the branching ratio of the Cabibbo suppressed decay D^0\to \pi^-\mu^+\nu relative to the Cabibbo favored decay D^0\to K^-\mu^+\nu and an improved measurement of the ratio |\frac{f_+^{\pi}(0)}{f_+^{K}(0)}|. Our results are 0.074 \pm 0.008 \pm 0.007 for the branching ratio and 0.85 \pm 0.04 \pm 0.04 \pm 0.01 for the form factor ratio, respectively.Comment: 13pages, 3 figure

Study of the D^0 \to pi^-pi^+pi^-pi^+ decay

Using data from the FOCUS (E831) experiment at Fermilab, we present new measurements for the Cabibbo-suppressed decay mode $D^0 \to \pi^-\pi^+\pi^-\pi^+$. We measure the branching ratio $\Gamma(D^0 \to\pi^+\pi^- \pi^+\pi^-)/\Gamma(D^0 \to K^-\pi^+\pi^-\pi^+) = 0.0914 \pm 0.0018 \pm 0.0022$. An amplitude analysis has been performed, a first for this channel, in order to determine the resonant substructure of this decay mode. The dominant component is the decay $D^0 \to a_1(1260)^+ \pi^-$, accounting for 60% of the decay rate. The second most dominant contribution comes from the decay $D^0 \to \rho(770)^0\rho(770)^0$, with a fraction of 25%. We also study the $a_1(1260)$ line shape and resonant substructure. Using the helicity formalism for the angular distribution of the decay $D^0 \to \rho(770)^0\rho(770)^0$, we measure a longitudinal polarization of $P_L = (71 \pm 4\pm 2)$%.Comment: 38 pages, 8 figures. accepted for publication in Physical Review