Loop space and evolution of the light-like Wilson polygons

We address a connection between the energy evolution of the polygonal light-like Wilson exponentials and the geometry of the loop space with the gauge invariant Wilson loops of a variety of shapes being the fundamental degrees of freedom. The renormalization properties and the differential area evolution of these Wilson polygons are studied by making use of the universal Schwinger quantum dynamical approach. We discuss the appropriateness of the dynamical differential equations in the loop space to the study of the energy evolution of the collinear and transverse-momentum dependent parton distribution functions.Comment: 8 pages, 2 eps figures; needs ws-ijmpcs.cls (supplied). Invited talk presented at the QCD Evolution Workshop, May 14 - 17 (2012), Thomas Jefferson National Accelerator Facility, Newport News (VA), US

Atomic-scale visualization of quasiparticle interference on a type-II Weyl semimetal surface

We combine quasiparticle interference simulation (theory) and atomic resolution scanning tunneling spectro-microscopy (experiment) to visualize the interference patterns on a type-II Weyl semimetal Mo$_{x}$W$_{1-x}$Te$_2$ for the first time. Our simulation based on first-principles band topology theoretically reveals the surface electron scattering behavior. We identify the topological Fermi arc states and reveal the scattering properties of the surface states in Mo$_{0.66}$W$_{0.34}$Te$_2$. In addition, our result reveals an experimental signature of the topology via the interconnectivity of bulk and surface states, which is essential for understanding the unusual nature of this material.Comment: To appear in Phys. Rev. Let

On the probability of staying above a wall for the (2+1)-dimensional SOS model at low temperature

We obtain sharp asymptotics for the probability that the (2+1)-dimensional discrete SOS interface at low temperature is positive in a large region. For a square region $\Lambda$, both under the infinite volume measure and under the measure with zero boundary conditions around $\Lambda$, this probability turns out to behave like $\exp(-\tau_\beta(0) L \log L )$, with $\tau_\beta(0)$ the surface tension at zero tilt, also called step free energy, and $L$ the box side. This behavior is qualitatively different from the one found for continuous height massless gradient interface models.Comment: 21 pages, 6 figure

Local and global gestalt laws: A neurally based spectral approach

A mathematical model of figure-ground articulation is presented, taking into account both local and global gestalt laws. The model is compatible with the functional architecture of the primary visual cortex (V1). Particularly the local gestalt law of good continuity is described by means of suitable connectivity kernels, that are derived from Lie group theory and are neurally implemented in long range connectivity in V1. Different kernels are compatible with the geometric structure of cortical connectivity and they are derived as the fundamental solutions of the Fokker Planck, the Sub-Riemannian Laplacian and the isotropic Laplacian equations. The kernels are used to construct matrices of connectivity among the features present in a visual stimulus. Global gestalt constraints are then introduced in terms of spectral analysis of the connectivity matrix, showing that this processing can be cortically implemented in V1 by mean field neural equations. This analysis performs grouping of local features and individuates perceptual units with the highest saliency. Numerical simulations are performed and results are obtained applying the technique to a number of stimuli.Comment: submitted to Neural Computatio