Progress in Small x Resummation

I review recent theoretical progress in the resummation of small x contributions to the evolution of parton distributions, in view of its potential significance for accurate phenomenology at future colliders. I show that a consistent perturbative resummation of collinear and energy logs is now possible, and necessary if one wishes to use recent NNLO results in the HERA kinematic region.Comment: 8 pages, 6 figures, LaTeX with IJMPA document class, invited plenary talk at the conference on QCD and hadronic physics, Beijing 200

Transmission lines and resonators based on quantum Hall plasmonics: electromagnetic field, attenuation and coupling to qubits

Quantum Hall edge states have some characteristic features that can prove useful to measure and control solid state qubits. For example, their high voltage to current ratio and their dissipationless nature can be exploited to manufacture low-loss microwave transmission lines and resonators with a characteristic impedance of the order of the quantum of resistance $h/e^2\sim 25\mathrm{k\Omega}$. The high value of the impedance guarantees that the voltage per photon is high and for this reason high impedance resonators can be exploited to obtain larger values of coupling to systems with a small charge dipole, e.g. spin qubits. In this paper, we provide a microscopic analysis of the physics of quantum Hall effect devices capacitively coupled to external electrodes. The electrical current in these devices is carried by edge magnetoplasmonic excitations and by using a semiclassical model, valid for a wide range of quantum Hall materials, we discuss the spatial profile of the electromagnetic field in a variety of situations of interest. Also, we perform a numerical analysis to estimate the lifetime of these excitations and, from the numerics, we extrapolate a simple fitting formula which quantifies the $Q$ factor in quantum Hall resonators. We then explore the possibility of reaching the strong photon-qubit coupling regime, where the strength of the interaction is higher than the losses in the system. We compute the Coulomb coupling strength between the edge magnetoplasmons and singlet-triplet qubits, and we obtain values of the coupling parameter of the order $100\mathrm{MHz}$; comparing these values to the estimated attenuation in the resonator, we find that for realistic qubit designs the coupling can indeed be strong

A PDE-constrained optimization formulation for discrete fracture network flows

We investigate a new numerical approach for the computation of the 3D flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex 3D systems of planar fractures. The discretization within each fracture is performed independently of the discretization of the other fractures and of their intersections. Independent meshing process within each fracture is a very important issue for practical large scale simulations making easier mesh generation. Some numerical simulations are given to show the viability of the method. The resulting approach can be naturally parallelized for dealing with systems with a huge number of fractures

The dynamics of generalized Palatini Theories of Gravity

It is known that in f(R) theories of gravity with an independent connection which can be both non-metric and non symmetric, this connection can always be algebraically eliminated in favour of the metric and the matter fields, so long as it is not coupled to the matter explicitly. We show here that this is a special characteristic of f(R) actions, and it is not true for actions that include other curvature invariants. This contradicts some recent claims in the literature. We clarify the reasons of this contradiction.Comment: v1: 6 pages; v2: minor changes to match published versio

Self impedance matched Hall-effect gyrators and circulators

We present a model study of an alternative implementation of a two-port Hall-effect microwave gyrator. Our set-up involves three electrodes, one of which acts as a common ground for the others. Based on the capacitive-coupling model of Viola and DiVincenzo, we analyze the performance of the device and we predict that ideal gyration can be achieved at specific frequencies. Interestingly, the impedance of the three-terminal gyrator can be made arbitrarily small for certain coupling strengths, so that no auxiliary impedance matching is required. Although the bandwidth of the device shrinks as the impedance decreases, it can be improved by reducing the magnetic field; it can be realistically increased up to $150 \mathrm{MHz}$ at $50\mathrm{\Omega}$ by working at filling factor $\nu=10$. We examine also the effects of the parasitic capacitive coupling between electrodes and we find that, although in general they strongly influence the response of device, their effect is negligible at low impedance. Finally, we analyze an interferometric implementation of a circulator, which incorporates the gyrator in a Mach-Zender-like construction. Perfect circulation in both directions can be achieved, depending on frequency and on the details of the interferometer

A model study of present-day Hall-effect circulators

Stimulated by the recent implementation of a three-port Hall-effect microwave circulator of Mahoney et al. (MEA), we present model studies of the performance of this device. Our calculations are based on the capacitive-coupling model of Viola and DiVincenzo (VD). Based on conductance data from a typical Hall-bar device obtained from a two-dimensional electron gas (2DEG) in a magnetic field, we numerically solve the coupled field-circuit equations to calculate the expected performance of the circulator, as determined by the $S$ parameters of the device when coupled to 50$\Omega$ ports, as a function of frequency and magnetic field. Above magnetic fields of 1.5T, for which a typical 2DEG enters the quantum Hall regime (corresponding to a Landau-level filling fraction $\nu$ of 20), the Hall angle $\theta_H=\tan^{-1}\sigma_{xy}/\sigma_{xx}$ always remains close to $90^\circ$, and the $S$ parameters are close to the analytic predictions of VD for $\theta_H=\pi/2$. As anticipated by VD, MEA find the device to have rather high (k$\Omega$) impedance, and thus to be extremely mismatched to $50\Omega$, requiring the use of impedance matching. We incorporate the lumped matching circuits of MEA in our modeling and confirm that they can produce excellent circulation, although confined to a very small bandwidth. We predict that this bandwidth is significantly improved by working at lower magnetic field when the Landau index is high, e.g. $\nu=20$, and the impedance mismatch is correspondingly less extreme. Our modeling also confirms the observation of MEA that parasitic port-to-port capacitance can produce very interesting countercirculation effects

APFELgrid: a high performance tool for parton density determinations

We present a new software package designed to reduce the computational burden of hadron collider measurements in Parton Distribution Function (PDF) fits. The APFELgrid package converts interpolated weight tables provided by APPLgrid files into a more efficient format for PDF fitting by the combination with PDF and $\alpha_s$ evolution factors provided by APFEL. This combination significantly reduces the number of operations required to perform the calculation of hadronic observables in PDF fits and simplifies the structure of the calculation into a readily optimised scalar product. We demonstrate that our technique can lead to a substantial speed improvement when compared to existing methods without any reduction in numerical accuracy.Comment: 13 pages, 2 figures. Submitted to CPC. Code available from https://github.com/nhartland/APFELgri

Heat wave propagation in a nonlinear chain

We investigate the propagation of temperature perturbations in an array of coupled nonlinear oscillators at finite temperature. We evaluate the response function at equilibrium and show how the memory effects affect the diffusion properties. A comparison with nonequilibrium simulations reveals that the telegraph equation provides a reliable interpretative paradigm for describing quantitatively the propagation of a heat pulse at the macroscopic level. The results could be of help in understanding and modeling energy transport in individual nanotubes.Comment: Revised version, 1 fig. adde