Charging Spectrum of a Small Wigner Crystal Island

Charging of a clean two-dimensional island is studied in the regime of small concentration of electrons when they form the Wigner crystal. The number of electrons in the island is assumed to be not too big (N < 100). It is shown that the total energy of the island as a function of N has a quasi-periodic component of a universal shape, that is independent of the form of electron-electron interactions. These oscillations are caused by the combination of the geometric effects associated with packing of the triangular lattice into the circular island. These effects are: the shell effect, associated with starting a new crystalline row, and the so-called confinement polaronic effect. In the presence of close metallic gates, which eliminate the long-range part of the electron-electron interactions, the oscillations of the energy bring about simultaneous entering of the dot by a few electrons.Comment: 8 pages, Latex, 8 Postscript pages are include

Screening of a hypercritical charge in graphene

Screening of a large external charge in graphene is studied. The charge is assumed to be displaced away or smeared over a finite region of the graphene plane. The initial decay of the screened potential with distance is shown to follow the 3/2 power. It gradually changes to the Coulomb law outside of a hypercritical core whose radius is proportional to the external charge.Comment: (v1) 4 pages, 1 figure (v2) Much improved introduction; extended range of numeric

Higher twist jet broadening and classical propagation

The transverse broadening of jets produced in deep-inelastic scattering (DIS) off a large nucleus is studied in the collinear limit. A class of medium enhanced higher twist corrections are re-summed to calculate the transverse momentum distribution of the produced collinear jet. In contrast to previous approaches, resummation of the leading length enhanced higher twist corrections is shown to lead to a two dimensional diffusion equation for the transverse momentum of the propagating jet. Results for the average transverse momentum obtained from this approach are then compared to the broadening expected from a classical Langevin analysis for the propagation of the jet under the action of the fluctuating color Lorentz force inside the nucleons. The set of approximations that lead to identical results from the two approaches are outlined. The relationship between the momentum diffusion constant $D$ and the transport coefficient $\hat{q}$ is explicitly derived.Comment: 17 pages, 6 figures, revtex4, references added, typos corrected, discussion update

Hard collinear gluon radiation and multiple scattering in a medium

The energy loss of hard jets produced in the Deep-Inelastic scattering (DIS) off a large nucleus is considered in the collinear limit. In particular, the single gluon emission cross section due to multiple scattering in the medium is calculated. Calculations are carried out in the higher-twist scheme, which is extended to include contributions from multiple transverse scatterings on both the produced quark and the radiated gluon. The leading length enhanced parts of these power suppressed contributions are resummed. Various interferences between such diagrams lead to the Landau-Pomeranchuk-Migdal (LPM) effect. We resum the corrections from an arbitrary number of scatterings and isolate the leading contributions which are suppressed by one extra power of the hard scale $Q^{2}$. All powers of the emitted gluon forward momentum fraction $y$ are retained. We compare our results with the previous calculation of single scattering per emission in the higher-twist scheme as well as with multiple scattering resummations in other schemes. It is found that the leading ($1/Q^2$) contribution to the double differential gluon production cross section, in this approach, is equivalent to that obtained from the single scattering calculation once the transverse momentum of the final quark is integrated out. We comment on the generalization of this formalism to Monte-Carlo routines.Comment: 30 pages, 7 figures, revtex4, typos correcte

Photon bremsstrahlung and diffusive broadening of a hard jet

The photon bremsstrahlung rate from a quark jet produced in deep-inelastic scattering (DIS) off a large nucleus is studied in the collinear limit. The leading medium-enhanced higher twist corrections which describe the multiple scattering of the jet in the nucleus are re-summed to all orders of twist. The propagation of the jet in the absence of further radiative energy loss is shown to be governed by a transverse momentum diffusion equation. We compute the final photon spectrum in the limit of soft photons, taking into account the leading and next-to-leading terms in the photon momentum fraction y. In this limit, the photon spectrum in a physical gauge is shown to arise from two interfering sources: one where the initial hard scattering produces an off-shell quark which immediately radiates the photon and then undergoes subsequent soft re-scattering; alternatively the quark is produced on-shell and propagates through the medium until it is driven off-shell by re-scattering and radiates the photon. Our result has a simple formal structure as a product of the photon splitting function, the quark transverse momentum distribution coming from a diffusion equation and a dimensionless factor which encodes the effect of the interferences encountered by the propagating quark over the length of the medium. The destructive nature of such interferences in the small y limit are responsible for the origin of the Landau-Pomeranchuck-Migdal (LPM) effect. Along the way we also discuss possible implications for quark jets in hot nuclear matter.Comment: 24 pages, 3 figures, Revtex

Measuring subdiffusion parameters

We propose a method to extract from experimental data the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_\alpha$ which are defined by means of the relation $=2D_\alpha/\Gamma(1+\alpha) t^\alpha$ where $$ denotes a mean square displacement of a random walker starting from $x=0$ at the initial time $t=0$. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. Using such a system, we experimentally study a diffusion of glucose and sucrose in a gel solvent. We find a fully analytic solution of the fractional subdiffusion equation with the initial and boundary conditions representing the system under study. Confronting the experimental data with the derived formulas, we show a subdiffusive character of the sugar transport in gel solvent. We precisely determine the parameter $\alpha$, which is smaller than 1, and the subdiffusion coefficient $D_\alpha$.Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.

Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure

Cognitive demands of face monitoring: Evidence for visuospatial overload

Young children perform difficult communication tasks better face to face than when they cannot see one another (e.g., Doherty-Sneddon & Kent, 1996). However, in recent studies, it was found that children aged 6 and 10 years, describing abstract shapes, showed evidence of face-to-face interference rather than facilitation. For some communication tasks, access to visual signals (such as facial expression and eye gaze) may hinder rather than help children’s communication. In new research we have pursued this interference effect. Five studies are described with adults and 10- and 6-year-old participants. It was found that looking at a face interfered with children’s abilities to listen to descriptions of abstract shapes. Children also performed visuospatial memory tasks worse when they looked at someone’s face prior to responding than when they looked at a visuospatial pattern or at the floor. It was concluded that performance on certain tasks was hindered by monitoring another person’s face. It is suggested that processing of visual communication signals shares certain processing resources with the processing of other visuospatial information

The Absence of Positive Energy Bound States for a Class of Nonlocal Potentials

We generalize in this paper a theorem of Titchmarsh for the positivity of Fourier sine integrals. We apply then the theorem to derive simple conditions for the absence of positive energy bound states (bound states embedded in the continuum) for the radial Schr\"odinger equation with nonlocal potentials which are superposition of a local potential and separable potentials.Comment: 23 page

Universal Parametric Correlations of Eigenvalues of Random Matrix Ensemble

Eigenvalue correlations of random matrix ensembles as a function of an external perturbation are investigated vis the Dyson Brownian Motion Model in the situation where the level density has a hard edge singularity. By solving a linearized hydrodynamical equation, a universal dependence of the density-density correlator on the external field is found. As an application we obtain a formula for the variance of linear statistics with the parametric dependence exhibited as a Laplace transform.Comment: 23 pages, late