Momentum resolved tunneling into the Pfaffian and anti-Pfaffian edges

We calculate the electron spectral functions at the edges of the Moore-Read Pfaffian and anti-Pfaffian fractional quantum Hall states, in the clean limit. We show that their qualitative differences can be probed using momentum resolved tunneling, thus providing a method to unambiguously distinguish which one is realized in the fractional quantum Hall state observed at filling factor $\nu=5/2$. We further argue that edge reconstruction, which may be less important in the first excited Landau level (LL) than in the lowest LL, can also be detected this way if present.Comment: published versio

Painl\'eve III and a singular linear statistics in Hermitian random matrix ensembles I

In this paper, we study a certain linear statistics of the unitary Laguerre ensembles, motivated in part by an integrable quantum field theory at finite temperature. It transpires that this is equivalent to the characterization of a sequence of polynomials orthogonal with respect to the weight w(x)=w(x,s):=x^{\al}\rme^{-x}\rme^{-s/x}, \quad 0\leq x0, s>0, namely, the determination of the associated Hankel determinant and recurrence coefficients. Here $w(x,s)$ is the Laguerre weight x^{\al}\:\rme^{-x} 'perturbed' by a multiplicative factor \rme^{-s/x}, which induces an infinitely strong zero at the origin. For polynomials orthogonal on the unit circle, a particular example where there are explicit formulas, the weight of which has infinitely strong zeros, was investigated by Pollazcek and Szeg\"o many years ago. Such weights are said to be 'singular' or irregular due to the violation of the Szeg\"o condition. In our problem, the linear statistics is a sum of the reciprocal of positive random variables $\{x_j:j=1,..,,n\};$ $\sum_{j=1}^{n}1/x_j.$ We show that the moment generating function, or the Laplace transform of the probability density function of this linear statistics is expressed as the ratio of Hankel determinants and as an integral of the combination of a particular third Painlev\'e function.Comment: 29 page

Better 3D Inspection with Structured Illumination Part I: Signal Formation and Precision

For quality control in the factory, 3D-metrology faces increasing demands for high precision and for more space-bandwidth-speed-product SBSP (number of 3D-points/sec). As a potential solution, we will discuss Structured-Illumination Microscopy (SIM). We distinguish optically smooth and rough surfaces and develop a theoretical model of the signal formation for both surface species. This model is exploited to investigate the physical limits of the precision and to give rules to optimize the sensor parameters for best precision or high speed. This knowledge can profitably be combined with fast scanning strategies, to maximize the SBSP, which will be discussed in paper part II.Comment: 7 pages, 5 figures, submitted to Applied Optics on April 17, 201

The Spectral Invariant Approximation within Canopy Radiative Transfer to Support the Use of the EPIC/DSCOVR Oxygen B-band for Monitoring Vegetation

EPIC (Earth Polychromatic Imaging Camera) is a 10-channel spectroradiometer onboard DSCOVR (Deep Space Climate Observatory) spacecraft. In addition to the NIR (780 nm) and the ‘red’ (680 nm) channels, EPIC also has the O2 A-band (764±0.2 nm) and B-band (687.75±0.2 nm). The EPIC at-sensor Normalized Difference Vegetation Index (NDVI) is defined as the difference between NIR and ‘red’ channels normalized to their sum. However, the use of the O2 B-band instead of the ‘red’ channel mitigates the effect ofatmosphere on surface reflectance because it reduces contribution from the radiation scattered by theatmosphere. Applying the radiative transfer theory and the spectral invariant approximation to EPIC observations, we provide supportive arguments for using the O2 band instead of the red channel for monitoring the vegetation dynamics

Leptogenesis via Higgs Condensate Relaxation

An epoch of Higgs relaxation may occur in the early universe during or immediately following postinflationary reheating. It has recently been pointed out that leptogenesis may occur in minimal extensions of the Standard Model during this epoch. We analyse Higgs relaxation taking into account the effects of perturbative and non-perturbative decays of the Higgs condensate, and we present a detailed derivation of the relevant kinetic equations and of the relevant particle interaction cross sections. We identify the parameter space in which a sufficiently large asymmetry is generated.Comment: 18 pages, 14 figure