The Aharonov-Bohm Effect in the Fractional Quantum Hall Regime

We have investigated experimentally resonant tunnelling through single-particle states formed around an antidot by a magnetic field, in the fractional quantum Hall regime. For 1/3 filling factor around the antidot, Aharonov-Bohm oscillations are observed with the same magnetic field period as in the integer quantum Hall regime. All our measurements are consistent with quasiparticles of fractional charge e*. However, the results are also consistent with particles of any charge (>= e*) as the system must rearrange every time the flux enclosed increases by h/e.Comment: Postscript, 4 pages, gzipped (350 kB

On the ratio of consecutive gaps between primes

In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong form a 60 years old problem of Erd\"os, which asked whether the ratio of two consecutive primegaps can be infinitely often arbitrarily small, and arbitrarily large, respectively

Detection of Coulomb Charging around an Antidot

We have detected oscillations of the charge around a potential hill (antidot) in a two-dimensional electron gas as a function of a perpendicular magnetic field B. The field confines electrons around the antidot in closed orbits, the areas of which are quantised through the Aharonov-Bohm effect. Increasing B reduces each state's area, pushing electrons closer to the centre, until enough charge builds up for an electron to tunnel out. This is a new form of the Coulomb blockade seen in electrostatically confined dots. We have also studied h/2e oscillations and found evidence for coupling of opposite spin states of the lowest Landau level.Comment: 3 pages, 3 Postscript figures, submitted to the proceedings of EP2DS-1

Probing e-e interactions in a periodic array of GaAs quantum wires

We present the results of non-linear tunnelling spectroscopy between an array of independent quantum wires and an adjacent two-dimensional electron gas (2DEG) in a double-quantum-well structure. The two layers are separately contacted using a surface-gate scheme, and the wires are all very regular, with dimensions chosen carefully so that there is minimal modulation of the 2DEG by the gates defining the wires. We have mapped the dispersion spectrum of the 1D wires down to the depletion of the last 1D subband by measuring the conductance \emph{G} as a function of the in-plane magnetic field \emph{B}, the interlayer bias $V_{\rm dc}$ and the wire gate voltage. There is a strong suppression of tunnelling at zero bias, with temperature and dc-bias dependences consistent with power laws, as expected for a Tomonaga-Luttinger Liquid caused by electron-electron interactions in the wires. In addition, the current peaks fit the free-electron model quite well, but with just one 1D subband there is extra structure that may indicate interactions.Comment: 3 pages, 3 figures; formatting correcte

Geometric Suppression of Single-Particle Energy Spacings in Quantum Antidots

Quantum Antidot (AD) structures have remarkable properties in the integer quantum Hall regime, exhibiting Coulomb-blockade charging and the Kondo effect despite their open geometry. In some regimes a simple single-particle (SP) model suffices to describe experimental observations while in others interaction effects are clearly important, although exactly how and why interactions emerge is unclear. We present a combination of experimental data and the results of new calculations concerning SP orbital states which show how the observed suppression of the energy spacing between states can be explained through a full consideration of the AD potential, without requiring any effects due to electron interactions such as the formation of compressible regions composed of multiple states, which may occur at higher magnetic fields. A full understanding of the regimes in which these effects occur is important for the design of devices to coherently manipulate electrons in edge states using AD resonances.Comment: 4 pages, 2 figure

One-Loop Renormalization of a Self-Interacting Scalar Field in Nonsimply Connected Spacetimes

Using the effective potential, we study the one-loop renormalization of a massive self-interacting scalar field at finite temperature in flat manifolds with one or more compactified spatial dimensions. We prove that, owing to the compactification and finite temperature, the renormalized physical parameters of the theory (mass and coupling constant) acquire thermal and topological contributions. In the case of one compactified spatial dimension at finite temperature, we find that the corrections to the mass are positive, but those to the coupling constant are negative. We discuss the possibility of triviality, i.e. that the renormalized coupling constant goes to zero at some temperature or at some radius of the compactified spatial dimension.Comment: 16 pages, plain LATE

The cost of simplifying air travel when modeling disease spread

Background: Air travel plays a key role in the spread of many pathogens. Modeling the long distance spread of infectious disease in these cases requires an air travel model. Highly detailed air transportation models can be over determined and computationally problematic. We compared the predictions of a simplified air transport model with those of a model of all routes and assessed the impact of differences on models of infectious disease. Methodology/Principal Findings: Using U.S. ticket data from 2007, we compared a simplified "pipe" model, in which individuals flow in and out of the air transport system based on the number of arrivals and departures from a given airport, to a fully saturated model where all routes are modeled individually. We also compared the pipe model to a "gravity" model where the probability of travel is scaled by physical distance; the gravity model did not differ significantly from the pipe model. The pipe model roughly approximated actual air travel, but tended to overestimate the number of trips between small airports and underestimate travel between major east and west coast airports. For most routes, the maximum number of false (or missed) introductions of disease is small (<1 per day) but for a few routes this rate is greatly underestimated by the pipe model. Conclusions/Significance: If our interest is in large scale regional and national effects of disease, the simplified pipe model may be adequate. If we are interested in specific effects of interventions on particular air routes or the time for the disease to reach a particular location, a more complex point-to-point model will be more accurate. For many problems a hybrid model that independently models some frequently traveled routes may be the best choice. Regardless of the model used, the effect of simplifications and sensitivity to errors in parameter estimation should be analyzed

Eccentricities of Planets in Binary Systems

The most puzzling property of the extrasolar planets discovered by recent radial velocity surveys is their high orbital eccentricities, which are very difficult to explain within our current theoretical paradigm for planet formation. Current data reveal that at least 25% of these planets, including some with particularly high eccentricities, are orbiting a component of a binary star system. The presence of a distant companion can cause significant secular perturbations in the orbit of a planet. At high relative inclinations, large-amplitude, periodic eccentricity perturbations can occur. These are known as "Kozai cycles" and their amplitude is purely dependent on the relative orbital inclination. Assuming that every planet host star also has a (possibly unseen, e.g., substellar) distant companion, with reasonable distributions of orbital parameters and masses, we determine the resulting eccentricity distribution of planets and compare it to observations? We find that perturbations from a binary companion always appear to produce an excess of planets with both very high (e>0.6) and very low (e<0.1) eccentricities. The paucity of near-circular orbits in the observed sample implies that at least one additional mechanism must be increasing eccentricities. On the other hand, the overproduction of very high eccentricities observed in our models could be combined with plausible circularization mechanisms (e.g., friction from residual gas) to create more planets with intermediate eccentricities (e=0.1-0.6).Comment: 8 pages, to appear in "Close Binaries in the 21st Century: New Opportunities and Challenges", ed. A. Gimenez et al. (Springer

Cold Feedback in Cooling-Flow Galaxy Clusters

We put forward an alternative view to the Bondi-driven feedback between heating and cooling of the intra-cluster medium (ICM) in cooling flow galaxies and clusters. We adopt the popular view that the heating is due to an active galactic nucleus (AGN), i.e. a central black hole accreting mass and launching jets and/or winds. We propose that the feedback occurs with the entire cool inner region (5-30 kpc). A moderate cooling flow does exist here, and non-linear over-dense blobs of gas cool fast and are removed from the ICM before experiencing the next major AGN heating event. Some of these blobs may not accrete on the central black hole, but may form stars and cold molecular clouds. We discuss the conditions under which the dense blobs may cool to low temperatures and feed the black hole.Comment: 6 pages, no figures, to appear in the Proceedings of "Heating vs. Cooling in Galaxies and Clusters of Galaxies", August 2006, Garching (Germany

Coherent oscillations and incoherent tunnelling in one - dimensional asymmetric double - well potential

For a model 1d asymmetric double-well potential we calculated so-called survival probability (i.e. the probability for a particle initially localised in one well to remain there). We use a semiclassical (WKB) solution of Schroedinger equation. It is shown that behaviour essentially depends on transition probability, and on dimensionless parameter which is a ratio of characteristic frequencies for low energy non-linear in-well oscillations and inter wells tunnelling. For the potential describing a finite motion (double-well) one has always a regular behaviour. For the small value of the parameter there is well defined resonance pairs of levels and the survival probability has coherent oscillations related to resonance splitting. However for the large value of the parameter no oscillations at all for the survival probability, and there is almost an exponential decay with the characteristic time determined by Fermi golden rule. In this case one may not restrict oneself to only resonance pair levels. The number of perturbed by tunnelling levels grows proportionally to the value of this parameter (by other words instead of isolated pairs there appear the resonance regions containing the sets of strongly coupled levels). In the region of intermediate values of the parameter one has a crossover between both limiting cases, namely the exponential decay with subsequent long period recurrent behaviour.Comment: 19 pages, 7 figures, Revtex, revised version. Accepted to Phys. Rev.