Two-particle scattering theory for anyons

We consider potential scattering theory of a nonrelativistic quantum mechanical 2-particle system in R^2 with anyon statistics. Sufficient conditions are given which guarantee the existence of wave operators and the unitarity of the S-matrix. As examples the rotationally invariant potential well and the delta-function potential are discussed in detail. In case of a general rotationally invariant potential the angular momentum decomposition leads to a theory of Jost functions. The anyon statistics parameter gives rise to an interpolation for angular momenta analogous to the Regge trajectories for complex angular momenta. Levinson's theorem is adapted to the present context. In particular we find that in case of a zero energy resonance the statistics parameter can be determined from the scattering phase.Comment: 42 pages of RevTex and 5 figures (included

Fully automatic worst-case execution time analysis for MATLAB/Simulink models

“This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder." “Copyright IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.”In today's technical world (e.g., in the automotive industry), more and more purely mechanical components get replaced by electro-mechanical ones. Thus the size and complexity of embedded systems steadily increases. To cope with this development, comfortable software engineering tools are being developed that allow a more functionality-oriented development of applications. The paper demonstrates how worst-case execution time (WCET) analysis is integrated into such a high-level application design and simulation tool MATLAB/Simulink-thus providing a higher-level interface to WCET analysis. The MATLAB/Simulink extensions compute and display worst-case timing data for all blocks of a MATLAB/Simulink simulation, which gives the developer of an application valuable feedback about the correct timing of the application being developed. The solution facilitates a fully-automated WCET analysis, i.e., in contrast to existing approaches the programmer does not have to provide path information

Symmetries of hadrons after unbreaking the chiral symmetry

We study hadron correlators upon artificial restoration of the spontaneously broken chiral symmetry. In a dynamical lattice simulation we remove the lowest lying eigenmodes of the Dirac operator from the valence quark propagators and study evolution of the hadron masses obtained. All mesons and baryons in our study, except for a pion, survive unbreaking the chiral symmetry and their exponential decay signals become essentially better. From the analysis of the observed spectroscopic patterns we conclude that confinement still persists while the chiral symmetry is restored. All hadrons fall into different chiral multiplets. The broken U(1)_A symmetry does not get restored upon unbreaking the chiral symmetry. We also observe signals of some higher symmetry that includes chiral symmetry as a subgroup. Finally, from comparison of the \Delta - N splitting before and after unbreaking of the chiral symmetry we conclude that both the color-magnetic and the flavor-spin quark-quark interactions are of equal importance.Comment: 12 pages, 14 figures; final versio

Evaluation of the hydrological cycle of MATCH driven by NCEP reanalysis data: comparison with GOME water vapor measurements

This study examines two key parameters of the hydrological cycle, water vapor (WV) and precipitation rates (PR), as modelled by the chemistry transport model MATCH (Model of Atmospheric Transport and Chemistry) driven by National Centers for Environmental Prediction (NCEP) reanalysis data (NRA). For model output evaluation we primarily employ WV total column data from the Global Ozone Monitoring Experiment (GOME) on ERS-2, which is the only instrument capable measuring WV on a global scale and over all surface types with a substantial data record from 1995 to the present. We find that MATCH and NRA WV and PR distributions are closely related, but that significant regional differences in both parameters exist in magnitude and distribution patterns when compared to the observations. We also find that WV residual patterns between model and observations show remarkable similarities to residuals observed in the PR when comparing MATCH and NRA output to observations comprised by the Global Precipitation Climatology Project (GPCP). We conclude that deficiencies in model parameters shared by MATCH and NRA, like in the surface evaporation rates and regional transport patterns, are likely to lead to the observed differences. Monthly average regional differences between MATCH modelled WV columns and the observations can be as large as 2 cm, based on the analysis of three years. Differences in the global mean WV values are, however, below 0.1 cm. Regional differences in the PR between MATCH and GPCP can be above 0.5 cm per day and MATCH computes on average a higher PR than what has been observed. The lower water vapor content of MATCH is related to shorter model WV residence times by up to 1 day as compared to the observations. We find that MATCH has problems in modelling the WV content in regions of strong upward convection like, for example, along the Inter Tropical Convergence Zone, where it appears to be generally too dry as compared to the observations. We discuss possible causes for this bias and demonstrate the value of the GOME WV record for model evaluation

Evaluation of the hydrological cycle of MATCH driven by NCEP reanalysis data: comparison with GOME water vapor field measurements

International audienceThis study examines two key parameters of the hydrological cycle, water vapor (WV) and precipitation rates (PR), as modelled by the chemistry transport model MATCH (Model of Atmospheric Transport and Chemistry) driven by National Centers for Environmental Prediction (NCEP) reanalysis data (NRA). For model output evaluation we employ WV total column data from the Global Ozone Monitoring Experiment (GOME) on ERS-2, which is the only instrument capable measuring WV on a global scale and over all surface types with a substantial data record from 1995 to the present. We find that MATCH and NRA WV and PR distributions are closely related, but that significant regional differences in both parameters exist in magnitude and distribution patterns when compared to the observations. We also find that WV residual patterns between model and observations show remarkable similarities to residuals observed in the PR when comparing MATCH and NRA output to observations comprised by the Global Precipitation Climatology Project (GPCP). We conclude that deficiencies in model parameters shared by MATCH and NRA, like, for example, in the evapotranspiration rates, are likely to lead to the observed differences. Regional differences between MATCH modelled WV columns and the observations can be as large as 2 cm on the basis of a three years monthly average. Differences in the global mean WV values are, however, below 1 mm. Regional differences in the PR between MATCH and GPCP can be above 5 mm per day and MATCH computes on average a higher PR than what has been observed. As a consequence, this leads to shorter model WV residence times by about 1 day as compared to NRA data and the observations. We find that MATCH has problems in modelling the WV content in regions of strong upward convection like, for example, along the Inter Tropical Convergence Zone, where it appears to be generally too dry as compared to the observations. The study therefore suggests that a too rapid conversion of WV to precipitate in MATCH, especially in instances of strong convection, leads to regionally too dry model results and in turn to generally too low WV residence times. The study additionally demonstrates the value of the GOME WV record for model evaluation

Alternative approach to computing transport coefficients: application to conductivity and Hall coefficient of hydrogenated amorphous silicon

We introduce a theoretical framework for computing transport coefficients for complex materials. As a first example, we resolve long-standing inconsistencies between experiment and theory pertaining to the conductivity and Hall mobility for amorphous silicon and show that the Hall sign anomaly is a consequence of localized states. Next, we compute the AC conductivity of amorphous polyanaline. The formalism is applicable to complex materials involving defects and band-tail states originating from static topological disorder and extended states. The method may be readily integrated with current \textit{ab initio} methods.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Photoemission spectra of many-polaron systems

The cross over from low to high carrier densities in a many-polaron system is studied in the framework of the one-dimensional spinless Holstein model, using unbiased numerical methods. Combining a novel quantum Monte Carlo approach and exact diagonalization, accurate results for the single-particle spectrum and the electronic kinetic energy on fairly large systems are obtained. A detailed investigation of the quality of the Monte Carlo data is presented. In the physically most important adiabatic intermediate electron-phonon coupling regime, for which no analytical results are available, we observe a dissociation of polarons with increasing band filling, leading to normal metallic behavior, while for parameters favoring small polarons, no such density-driven changes occur. The present work points towards the inadequacy of single-polaron theories for a number of polaronic materials such as the manganites.Comment: 15 pages, 13 figures; final version, accepted for publication in Phys. Rev.

Phase transition and phase diagram at a general filling in the spinless one-dimensional Holstein Model

Among the mechanisms for lattice structural deformation, the electron-phonon interaction mediated Peierls charge-density-wave (CDW) instability in single band low-dimensional systems is perhaps the most ubiquitous. The standard mean-field picture predicts that the CDW transition occurs at all fillings and all values of the electron-phonon coupling $g$ and the adiabaticity parameter $t/\omega_0$. Here, we correct the mean-field expression for the Peierls instability condition by showing that the non-interacting static susceptibility, at twice the Fermi momentum, should be replaced by the dynamic one. We derive the Luttinger liquid (LL) to CDW transition condition, {\it exact to second order in a novel blocked perturbative approach}, for the spinless one-dimensional Holstein model in the adiabatic regime. The small parameter is the ratio $g \omega_0/t$. We present the phase diagram at non-half-filling by obtaining the surprising result that the CDW occurs in a more restrictive region of a two parameter ($g^2 \omega_0/t$ and $t/\omega_0$) space than at half-filling.Comment: Made changes in the appendices and also in notatio

Diving Deep into Sentiment: Understanding Fine-tuned CNNs for Visual Sentiment Prediction

Visual media are powerful means of expressing emotions and sentiments. The constant generation of new content in social networks highlights the need of automated visual sentiment analysis tools. While Convolutional Neural Networks (CNNs) have established a new state-of-the-art in several vision problems, their application to the task of sentiment analysis is mostly unexplored and there are few studies regarding how to design CNNs for this purpose. In this work, we study the suitability of fine-tuning a CNN for visual sentiment prediction as well as explore performance boosting techniques within this deep learning setting. Finally, we provide a deep-dive analysis into a benchmark, state-of-the-art network architecture to gain insight about how to design patterns for CNNs on the task of visual sentiment prediction.Comment: Preprint of the paper accepted at the 1st Workshop on Affect and Sentiment in Multimedia (ASM), in ACM MultiMedia 2015. Brisbane, Australi