Stability of the selfsimilar dynamics of a vortex filament

In this paper we continue our investigation about selfsimilar solutions of the vortex filament equation, also known as the binormal flow (BF) or the localized induction equation (LIE). Our main result is the stability of the selfsimilar dynamics of small pertubations of a given selfsimilar solution. The proof relies on finding precise asymptotics in space and time for the tangent and the normal vectors of the perturbations. A main ingredient in the proof is the control of the evolution of weighted norms for a cubic 1-D Schr\"odinger equation, connected to the binormal flow by Hasimoto's transform.Comment: revised version, 36 page

Thermodynamical limit of general gl(N) spin chains: vacuum state and densities

We study the vacuum state of spin chains where each site carry an arbitrary representation. We prove that the string hypothesis, usually used to solve the Bethe ansatz equations, is valid for representations characterized by rectangular Young tableaux. In these cases, we obtain the density of the center of the strings for the vacuum. We work out different examples and, in particular, the spin chains with periodic array of impurities.Comment: Latex file, 27 pages, 5 figures (.eps) A more detailed study of the representations allowing string hypothesis has added. A simpler formula for the densities is given. References added and misprint correcte

Extremal dynamics model on evolving networks

We investigate an extremal dynamics model of evolution with a variable number of units. Due to addition and removal of the units, the topology of the network evolves and the network splits into several clusters. The activity is mostly concentrated in the largest cluster. The time dependence of the number of units exhibits intermittent structure. The self-organized criticality is manifested by a power-law distribution of forward avalanches, but two regimes with distinct exponents tau = 1.98 +- 0.04 and tau^prime = 1.65 +- 0.05 are found. The distribution of extinction sizes obeys a power law with exponent 2.32 +- 0.05.Comment: 4 pages, 5 figure

Cotangent bundle quantization: Entangling of metric and magnetic field

For manifolds $\cal M$ of noncompact type endowed with an affine connection (for example, the Levi-Civita connection) and a closed 2-form (magnetic field) we define a Hilbert algebra structure in the space $L^2(T^*\cal M)$ and construct an irreducible representation of this algebra in $L^2(\cal M)$. This algebra is automatically extended to polynomial in momenta functions and distributions. Under some natural conditions this algebra is unique. The non-commutative product over $T^*\cal M$ is given by an explicit integral formula. This product is exact (not formal) and is expressed in invariant geometrical terms. Our analysis reveals this product has a front, which is described in terms of geodesic triangles in $\cal M$. The quantization of $\delta$-functions induces a family of symplectic reflections in $T^*\cal M$ and generates a magneto-geodesic connection $\Gamma$ on $T^*\cal M$. This symplectic connection entangles, on the phase space level, the original affine structure on $\cal M$ and the magnetic field. In the classical approximation, the $\hbar^2$-part of the quantum product contains the Ricci curvature of $\Gamma$ and a magneto-geodesic coupling tensor.Comment: Latex, 38 pages, 5 figures, minor correction

Decoherence of Semiclassical Wigner Functions

The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation for this equation. The semiclassical description of the Wigner function in terms of chords, each with its classically defined amplitude and phase, is thus inserted in the integrals, which leads to an explicit differential equation for the Wigner function. All the Lindblad operators are assumed to be represented by smooth phase space functions corresponding to classical variables. In the case that these are real, representing hermitian operators, the semiclassical Lindblad equation can be integrated. There results a simple extension of the unitary evolution of the semiclassical Wigner function, which does not affect the phase of each chord contribution, while dampening its amplitude. This decreases exponentially, as governed by the time integral of the square difference of the Lindblad functions along the classical trajectories of both tips of each chord. The decay of the amplitudes is shown to imply diffusion in energy for initial states that are nearly pure. Projecting the Wigner function onto an orthogonal position or momentum basis, the dampening of long chords emerges as the exponential decay of off-diagonal elements of the density matrix.Comment: 23 pg, 2 fi

Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a generic gl(n)-spin chain possessing on each site an arbitrary gl(n)-representation. For open spin chains, we use the classification of the reflection matrices to treat all the diagonal boundary cases. As a result, we obtain the Bethe equations in their full generality for closed and open spin chains. The classifications of finite dimensional irreducible representations for the Yangian (closed spin chains) and for the reflection algebras (open spin chains) are directly linked to the calculation of the transfer matrix eigenvalues. As examples, we recover the usual closed and open spin chains, we treat the alternating spin chains and the closed spin chain with impurity

Measurements of differential and double-differential Drell-Yan cross sections in proton-proton collisions at [Formula: see text][Formula: see text].

Measurements of the differential and double-differential Drell-Yan cross sections in the dielectron and dimuon channels are presented. They are based on proton-proton collision data at [Formula: see text] recorded with the CMS detector at the LHC and corresponding to an integrated luminosity of 19.7[Formula: see text]. The measured inclusive cross section in the [Formula: see text] peak region (60-120[Formula: see text]), obtained from the combination of the dielectron and dimuon channels, is [Formula: see text], where the statistical uncertainty is negligible. The differential cross section [Formula: see text] in the dilepton mass range 15-2000[Formula: see text] is measured and corrected to the full phase space. The double-differential cross section [Formula: see text] is also measured over the mass range 20 to 1500[Formula: see text] and absolute dilepton rapidity from 0 to 2.4. In addition, the ratios of the normalized differential cross sections measured at [Formula: see text] and 8[Formula: see text] are presented. These measurements are compared to the predictions of perturbative QCD at next-to-leading and next-to-next-to-leading (NNLO) orders using various sets of parton distribution functions (PDFs). The results agree with the NNLO theoretical predictions computed with fewz 3.1 using the CT10 NNLO and NNPDF2.1 NNLO PDFs. The measured double-differential cross section and ratio of normalized differential cross sections are sufficiently precise to constrain the proton PDFs

Search for physics beyond the standard model in events with τ leptons, jets, and large transverse momentum imbalance in pp collisions at [Formula: see text].

A search for physics beyond the standard model is performed with events having one or more hadronically decaying τ leptons, highly energetic jets, and large transverse momentum imbalance. The data sample corresponds to an integrated luminosity of 4.98 fb-1 of proton-proton collisions at [Formula: see text] collected with the CMS detector at the LHC in 2011. The number of observed events is consistent with predictions for standard model processes. Lower limits on the mass of the gluino in supersymmetric models are determined