Weak local rules for planar octagonal tilings

We provide an effective characterization of the planar octagonal tilings which admit weak local rules. As a corollary, we show that they are all based on quadratic irrationalities, as conjectured by Thang Le in the 90s.Comment: 23 pages, 6 figure

π\pi and σ\sigma mesons at finite temperature and density in the NJL model with dimensional regularization

Dynamical Symmetry breaking and meson masses are studied in the Nambu-Jona-Lasinio (NJL) model at finite temperature and chemical potential using the dimensional regularization. Since the model is not renormalizable in four space-time dimensions, physical results and parameters depend on the regularization method. Following the imaginary time formalism, we introduce the temperature, $T$ and the chemical potential, $\mu$. The parameters in the model are fixed by calculating the pion mass and decay constant in the dimensional regularization at $T=\mu=0$.Comment: 28 pages, 9 figures, v2: a few points corrected and references adde

Power allocation in wireless multi-user relay networks

In this paper, we consider an amplify-and-forward wireless relay system where multiple source nodes communicate with their corresponding destination nodes with the help of relay nodes. Conventionally, each relay equally distributes the available resources to its relayed sources. This approach is clearly sub-optimal since each user experiences dissimilar channel conditions, and thus, demands different amount of allocated resources to meet its quality-of-service (QoS) request. Therefore, this paper presents novel power allocation schemes to i) maximize the minimum signal-to-noise ratio among all users; ii) minimize the maximum transmit power over all sources; iii) maximize the network throughput. Moreover, due to limited power, it may be impossible to satisfy the QoS requirement for every user. Consequently, an admission control algorithm should first be carried out to maximize the number of users possibly served. Then, optimal power allocation is performed. Although the joint optimal admission control and power allocation problem is combinatorially hard, we develop an effective heuristic algorithm with significantly reduced complexity. Even though theoretically sub-optimal, it performs remarkably well. The proposed power allocation problems are formulated using geometric programming (GP), a well-studied class of nonlinear and nonconvex optimization. Since a GP problem is readily transformed into an equivalent convex optimization problem, optimal solution can be obtained efficiently. Numerical results demonstrate the effectiveness of our proposed approach

Two Distinct Electronic Contributions in the Fully Symmetric Raman Response of High TcT_{c} Cuprates

We show by non resonant effect in HgBa$_2$CuO$_{4+\delta}$ (Hg-1201)and by Zn substitutions in YBa$_2$Cu$_3$O$_{7-\delta}$ (Y-123) compounds that the fully symmetric Raman spectrum has two distinct electronic contributions. The A$_{1g}$ response consists in the superconducting pair breaking peak at the 2$\Delta$ energy and a collective mode close to the magnetic resonance energy. These experimental results reconcile the \textit{d-wave} model to the A$_{1g}$ Raman response function in so far as a collective mode that is distinct from the pair breaking peak is present in the A$_{1g}$ channel.Comment: 4 pages, 2 figure

Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light

It is theoretically shown that nanometric silver lamellar gratings present very strong visible light absorption inside the grooves, leading to electric field intensities by several orders of magnitude larger than that of the impinging light. This effect, due to the excitation of long wave vector surface plasmon polaritons with particular small penetration depth in the metal, may explain the abnormal optical absorption observed a long time ago on almost flat Ag films. Surface enhanced Raman scattering in rough metallic films could also be due to the excitation of such plasmon polaritons in the grain boundaries or notches of the films.Comment: 5 pages, 5 figure, submitted to Phys. Rev. Let

An experimental proposal to study collapse of the wave function in travelling-wave parametric amplifiers

The read-out of a microwave qubit state occurs using an amplification chain that enlarges the quantum state to a signal detectable with a classical measurement apparatus. However, at what point in this process did we really `measure' the quantum state? In order to investigate whether the `measurement' takes place in the amplification chain, we propose to construct a microwave interferometer that has a parametric amplifier added to each of its arms. Feeding the interferometer with single photons, the visibility depends on the gain of the amplifiers and whether a measurement collapse has taken place during the amplification process. We calculate the interference visibility as given by standard quantum mechanics as a function of gain, insertion loss and temperature and find a magnitude of $1/3$ in the limit of large gain without taking into account losses. This number reduces to $0.26$ in case the insertion loss of the amplifiers is $2.2$ dB at a temperature of $50$ mK. We show that if the wave function collapses within the interferometer, we will measure a reduced visibility compared to the prediction from standard quantum mechanics once this collapse process sets in.Comment: 21 pages and 23 figures (including appendices and subfigures). v4: Abstract and introduction rewritten and note on stochasticity of quantum state collapse added to section 6. v5: no content changes w.r.t. v