IFSM representation of Brownian motion with applications to simulation

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L2 decomposition like the Kac-Siegert/Karnounen-Loeve series. In this paper we first propose a IFSM (Iterated Function Systems with Maps) operator whose fixed point is the trajectory of the BM. We then use this representation of the process to simulate its trajectories. The resulting simulated trajectories are self-affine, continuous and fractal by construction. This fact produces more realistic trajectories than other schemes in the sense that their geometry is closer to the one of the true BM's trajectories. The IFSM trajectory of the BM can then be used to generate more realistic solutions of stochastic differential equations

Symmetries of the Einstein Equations

Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, \ie at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions and find that the only generalized symmetry transformations consist of: (i) constant scalings of the metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ``observables'' for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.Comment: 15 pages, FTG-114-USU, Plain Te

Transverse-momentum resummation for heavy-quark hadroproduction

We consider the production of a pair of heavy quarks ($Q{\bar Q}$) in hadronic collisions. When the transverse momentum $q_T$ of the heavy-quark pair is much smaller than its invariant mass, the QCD perturbative expansion is affected by large logarithmic terms that must be resummed to all-orders. This behavior is well known from the simpler case of hadroproduction of colourless high-mass systems, such as vector or Higgs boson(s). In the case of $Q{\bar Q}$ production, the final-state heavy quarks carry colour charge and are responsible for additional soft radiation (through direct emission and interferences with initial-state radiation) that complicates the evaluation of the logarithmically-enhanced terms in the small-$q_T$ region. We present the all-order resummation structure of the logarithmic contributions, which includes colour flow evolution factors due to soft wide-angle radiation. Resummation is performed at the completely differential level with respect to the kinematical variables of the produced heavy quarks. Soft-parton radiation produces azimuthal correlations that are fully taken into account by the resummation formalism. These azimuthal correlations are entangled with those that are produced by initial-state collinear radiation. We present explicit analytical results up to next-to-leading order and next-to-next-to-leading logarithmic accuracy.Comment: Some comments expanded and references added. Version published on NP

Translation-Rotation Coupling in Transient Grating Experiments : Theoretical and Experimental Evidences

The results of a Transient Grating experiment in a supercooled molecular liquid of anisotropic molecules and its theoretical interpretation are presented. These results show the existence of two distinct dynamical contributions in the response function of this experiment, density and orientation dynamics. These dynamics can be experimentally disentangled by varying the polarisation of the probe and diffracted beams and they have been identified and measured in a Heterodyne Detected experiment performed on m-toluidine. The results of the theory show a good qualitative agreement with the measurements at all temperatures.Comment: PDF format, 14 pages including 4 figures, accepted for publication in EPL. minor modification

Non-local transport and the Hall viscosity of 2D hydrodynamic electron liquids

In a fluid subject to a magnetic field the viscous stress tensor has a dissipationless antisymmetric component controlled by the so-called Hall viscosity. We here propose an all-electrical scheme that allows a determination of the Hall viscosity of a two-dimensional electron liquid in a solid-state device.Comment: 12 pages, 4 figure

Gurses' Type (b) Transformations are Neighborhood-Isometries

Following an idea close to one given by C. G. Torre (private communication), we prove that Riemannian spaces (M,g) and (M,h) that are related by a Gurses type (b) transformation [M. Gurses, Phys. Rev. Lett. 70, 367 (1993)] or, equivalently, by a Torre-Anderson generalized diffeomorphism [C. G. Torre and I. M. Anderson, Phys. Rev. Lett. xx, xxx (1993)] are neighborhood-isometric, i.e., every point x in M has a corresponding diffeomorphism phi of a neighborhood V of x onto a generally different neighborhood W of x such that phi*(h|W) = g|V.Comment: 10 pages, LATEX, FJE-93-00