Paired composite fermion wavefunctions

We construct a family of BCS paired composite fermion wavefunctions that generalize, but remain in the same topological phase as, the Moore-Read Pfaffian state for the half-filled Landau level. It is shown that for a wide range of experimentally relevant inter-electron interactions the groundstate can be very accurately represented in this form.Comment: 4 pages, 2 figure

Social Network Games with Obligatory Product Selection

Recently, Apt and Markakis introduced a model for product adoption in social networks with multiple products, where the agents, influenced by their neighbours, can adopt one out of several alternatives (products). To analyze these networks we introduce social network games in which product adoption is obligatory. We show that when the underlying graph is a simple cycle, there is a polynomial time algorithm allowing us to determine whether the game has a Nash equilibrium. In contrast, in the arbitrary case this problem is NP-complete. We also show that the problem of determining whether the game is weakly acyclic is co-NP hard. Using these games we analyze various types of paradoxes that can arise in the considered networks. One of them corresponds to the well-known Braess paradox in congestion games. In particular, we show that social networks exist with the property that by adding an additional product to a specific node, the choices of the nodes will unavoidably evolve in such a way that everybody is strictly worse off.Comment: In Proceedings GandALF 2013, arXiv:1307.416

Wigner distributions for finite dimensional quantum systems: An algebraic approach

We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space', and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail.Comment: Latex, 13 page

Phase-space descriptions of operators and the Wigner distribution in quantum mechanics II. The finite dimensional case

A complete solution to the problem of setting up Wigner distribution for N-level quantum systems is presented. The scheme makes use of some of the ideas introduced by Dirac in the course of defining functions of noncommuting observables and works uniformly for all N. Further, the construction developed here has the virtue of being essentially input-free in that it merely requires finding a square root of a certain N^2 x N^2 complex symmetric matrix, a task which, as is shown, can always be accomplished analytically. As an illustration, the case of a single qubit is considered in some detail and it is shown that one recovers the result of Feynman and Wootters for this case without recourse to any auxiliary constructs.Comment: 14 pages, typos corrected, para and references added in introduction, submitted to Jour. Phys.

Use of an audio-paced incremental swimming test in young national-level swimmers

Purpose:To evaluate the reliability and sensitivity to training of an audio-paced incremental swimming test.Methods:Eight young national-level male swimmers (age 15 ± 1 year) performed a 7 × 200-m incremental swimming test (velocities 1.19, 1.24, 1.28, 1.33, 1.39, and 1.45 m/s and maximal sprint pace) using an audio-pacing device. The same test was performed 4 times by each participant, 1 wk apart to assess reliability (WK1, WK2) and after 9 and 20 wk of training (WK9, WK20). Blood lactate concentration ([La−]) and heart rate (HR) were recorded after each stage. Outcome measures were the velocity (v) and HR at lactate markers of 2 mM, 4 mM, and Δ1 mM.Results:Velocities at the lactate markers proved to be more reliable than HR, with typical errors ranging from 0.66% to 2.30% and 1.28% to 4.50%, respectively (shifts in mean ranged –0.91% to 0.73% and –0.84% to 1.79%, respectively). Across WK1, WK9, and WK20 there were significant improvements in peak velocity (P &lt; .001) and each of the velocities associated with the lactate markers (P &lt; .05), whereas only HR at Δ1 mM improved (P &lt; .05).Conclusions:This article demonstrates that an audio-paced incremental swimming test is reliable for use with junior swimmers and is sensitive to changes observed after training. The postswimming measurement of HR in the pool was comparatively less reliable.</jats:sec

Wigner-Weyl isomorphism for quantum mechanics on Lie groups

The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie group $G$ is developed in detail. Several New features are shown to arise which have no counterparts in the familiar Cartesian case. Notable among these is the notion of a `semiquantised phase space', a structure on which the Weyl symbols of operators turn out to be naturally defined and, figuratively speaking, located midway between the classical phase space $T^*G$ and the Hilbert space of square integrable functions on $G$. General expressions for the star product for Weyl symbols are presented and explicitly worked out for the angle-angular momentum case.Comment: 32 pages, Latex2

Study to investigate and evaluate means of optimizing the Ku-band communication function for the space shuttle

The forward link of the overall Ku-band communication system consists of the ground- TDRS-orbiter communication path. Because the last segment of the link is directed towards a relatively low orbiting shuttle, a PN code is used to reduce the spectral density. A method is presented for incorporating code acquisition and tracking functions into the orbiter's Ku-band receiver. Optimization of a three channel multiplexing technique is described. The importance of Costas loop parameters to provide false lock immunity for the receiver, and the advantage of using a sinusoidal subcarrier waveform, rather than square wave, are discussed