Note on lattice regularization and equal-time correlators for parton distribution functions

We show that a recent interesting idea to circumvent the difficulties with the continuation of parton distribution functions to the Euclidean region, that consists in looking at equal time correlators between proton states of infinite momentum, encounters some problems related to the power divergent mixing pattern of DIS operators, when implemented within the lattice regularization.Comment: 15 pages, no figures, Physical Review D (2017

Hilbert Functions of Filtered Modules

In this presentation we shall deal with some aspects of the theory of Hilbert functions of modules over local rings, and we intend to guide the reader along one of the possible routes through the last three decades of progress in this area of dynamic mathematical activity. Motivated by the ever increasing interest in this field, our goal is to gather together many new developments of this theory into one place, and to present them using a unifying approach which gives self-contained and easier proofs. In this text we shall discuss many results by different authors, following essentially the direction typified by the pioneering work of J. Sally. Our personal view of the subject is most visibly expressed by the presentation of Chapters 1 and 2 in which we discuss the use of the superficial elements and related devices. Basic techniques will be stressed with the aim of reproving recent results by using a more elementary approach. Over the past few years several papers have appeared which extend classical results on the theory of Hilbert functions to the case of filtered modules. The extension of the theory to the case of general filtrations on a module has one more important motivation. Namely, we have interesting applications to the study of graded algebras which are not associated to a filtration, in particular the Fiber cone and the Sally-module. We show here that each of these algebras fits into certain short exact sequences, together with algebras associated to filtrations. Hence one can study the Hilbert function and the depth of these algebras with the aid of the know-how we got in the case of a filtration.Comment: 127 pages, revised version. Comments and remarks are welcom

Quantum Cloning by Cellular Automata

We introduce a quantum cellular automaton that achieves approximate phase-covariant cloning of qubits. The automaton is optimized for 1-to-2N economical cloning. The use of the automaton for cloning allows us to exploit different foliations for improving the performance with given resources.Comment: 4 pages, 6 figures, 1 table, published versio

Lateral conduction effects on heat-transfer data obtained with the phase-change paint technique

A computerized tool, CAPE, (Conduction Analysis Program using Eigenvalues) has been developed to account for lateral heat conduction in wind tunnel models in the data reduction of the phase-change paint technique. The tool also accounts for the effects of finite thickness (thin wings) and surface curvature. A special reduction procedure using just one time of melt is also possible on leading edges. A novel iterative numerical scheme was used, with discretized spatial coordinates but analytic integration in time, to solve the inverse conduction problem involved in the data reduction. A yes-no chart is provided which tells the test engineer when various corrections are large enough so that CAPE should be used. The accuracy of the phase-change paint technique in the presence of finite thickness and lateral conduction is also investigated

Linear and nonlinear evolution of current-carrying highly magnetized jets

We investigate the linear and nonlinear evolution of current-carrying jets in a periodic configuration by means of high resolution three-dimensional numerical simulations. The jets under consideration are strongly magnetized with a variable pitch profile and initially in equilibrium under the action of a force-free magnetic field. The growth of current-driven (CDI) and Kelvin-Helmholtz (KHI) instabilities is quantified using three selected cases corresponding to static, Alfvenic and super-Alfvenic jets. During the early stages, we observe large-scale helical deformations of the jet corresponding to the growth of the initially excited CDI mode. A direct comparison between our simulation results and the analytical growth rates obtained from linear theory reveals good agreement on condition that high-resolution and accurate discretization algorithms are employed. After the initial linear phase, the jet structure is significantly altered and, while slowly-moving jets show increasing helical deformations, larger velocity shear are violently disrupted on a few Alfven crossing time leaving a turbulent flow structure. Overall, kinetic and magnetic energies are quickly dissipated into heat and during the saturated regime the jet momentum is redistributed on a larger surface area with most of the jet mass travelling at smaller velocities. The effectiveness of this process is regulated by the onset of KHI instabilities taking place at the jet/ambient interface and can be held responsible for vigorous jet braking and entrainment.Comment: 14 pages, 11 figure

Experimental reconstruction of photon statistics without photon counting

Experimental reconstructions of photon number distributions of both continuous-wave and pulsed light beams are reported. Our scheme is based on on/off avalanche photodetection assisted by maximum-likelihood estimation and does not involve photon counting. Reconstructions of the distribution for both semiclassical and quantum states of light are reported for single-mode as well as for multimode beams.Comment: Revised version: in press on PRL. 4 pages, 4 fig

On lattice chiral gauge theories

The Smit-Swift-Aoki formulation of a lattice chiral gauge theory is presented. In this formulation the Wilson and other non invariant terms in the action are made gauge invariant by the coupling with a nonlinear auxilary scalar field, omega. It is shown that omega decouples from the physical states only if appropriate parameters are tuned so as to satisfy a set of BRST identities. In addition, explicit ghost fields are necessary to ensure decoupling. These theories can give rise to the correct continuum limit. Similar considerations apply to schemes with mirror fermions. Simpler cases with a global chiral symmetry are discussed and it is shown that the theory becomes free at decoupling. Recent numerical simulations agree with those considerations