Edge scaling limits for a family of non-Hermitian random matrix ensembles

A family of random matrix ensembles interpolating between the GUE and the Ginibre ensemble of $n\times n$ matrices with iid centered complex Gaussian entries is considered. The asymptotic spectral distribution in these models is uniform in an ellipse in the complex plane, which collapses to an interval of the real line as the degree of non-Hermiticity diminishes. Scaling limit theorems are proven for the eigenvalue point process at the rightmost edge of the spectrum, and it is shown that a non-trivial transition occurs between Poisson and Airy point process statistics when the ratio of the axes of the supporting ellipse is of order $n^{-1/3}$. In this regime, the family of limiting probability distributions of the maximum of the real parts of the eigenvalues interpolates between the Gumbel and Tracy-Widom distributions.Comment: 44 page

Internally Electrodynamic Particle Model: Its Experimental Basis and Its Predictions

The internally electrodynamic (IED) particle model was derived based on overall experimental observations, with the IED process itself being built directly on three experimental facts, a) electric charges present with all material particles, b) an accelerated charge generates electromagnetic waves according to Maxwell's equations and Planck energy equation and c) source motion produces Doppler effect. A set of well-known basic particle equations and properties become predictable based on first principles solutions for the IED process; several key solutions achieved are outlined, including the de Broglie phase wave, de Broglie relations, Schr\"odinger equation, mass, Einstein mass-energy relation, Newton's law of gravity, single particle self interference, and electromagnetic radiation and absorption; these equations and properties have long been broadly experimentally validated or demonstrated. A specific solution also predicts the Doebner-Goldin equation which emerges to represent a form of long-sought quantum wave equation including gravity. A critical review of the key experiments is given which suggests that the IED process underlies the basic particle equations and properties not just sufficiently but also necessarily.Comment: Presentation at the 27th Int Colloq on Group Theo Meth in Phys, 200

Constrained simulations of the Antennae Galaxies: Comparison with Herschel-PACS observations

We present a set of hydro-dynamical numerical simulations of the Antennae galaxies in order to understand the origin of the central overlap starburst. Our dynamical model provides a good match to the observed nuclear and overlap star formation, especially when using a range of rather inefficient stellar feedback efficiencies (0.01 < q_EoS < 0.1). In this case a simple conversion of local star formation to molecular hydrogen surface density motivated by observations accounts well for the observed distribution of CO. Using radiative transfer post-processing we model synthetic far-infrared spectral energy distributions (SEDs) and two-dimensional emission maps for direct comparison with Herschel-PACS observations. For a gas-to-dust ratio of 62:1 and the best matching range of stellar feedback efficiencies the synthetic far-infrared SEDs of the central star forming region peak at values of ~65 - 81 Jy at 99 - 116 um, similar to a three-component modified black body fit to infrared observations. Also the spatial distribution of the far-infrared emission at 70 um, 100 um, and 160 um compares well with the observations: >50% (> 35%) of the emission in each band is concentrated in the overlap region while only < 30% (< 15%) is distributed to the combined emission from the two galactic nuclei in the simulations (observations). As a proof of principle we show that parameter variations in the feedback model result in unambiguous changes both in the global and in the spatially resolved observable far-infrared properties of Antennae galaxy models. Our results strengthen the importance of direct, spatially resolved comparative studies of matched galaxy merger simulations as a valuable tool to constrain the fundamental star formation and feedback physics.Comment: 17 pages, 8 figures, 4 tables, submitted to MNRAS, including revisions after first referee report, comments welcom

Cyclotron resonance lineshape in a Wigner crystal

The cyclotron resonance absorption spectrum in a Wigner crystal is calculated. Effects of spin-splitting are modelled by substitutional disorder, and calculated in the coherent potential approximation. Due to the increasing strength of the dipole-dipole interaction, the results show a crossover from a double-peak spectrum at small filling factors to a single-peak spectrum at filling factors \agt 1/6. Radiation damping and magnetophonon scattering can also influence the cyclotron resonance. The results are in very good agreement with experiments.Comment: 4 pages REVTEX, attempt to append 3 figures that seem to have been lost last tim

Applications and generalizations of Fisher-Hartwig asymptotics

Fisher-Hartwig asymptotics refers to the large $n$ form of a class of Toeplitz determinants with singular generating functions. This class of Toeplitz determinants occurs in the study of the spin-spin correlations for the two-dimensional Ising model, and the ground state density matrix of the impenetrable Bose gas, amongst other problems in mathematical physics. We give a new application of the original Fisher-Hartwig formula to the asymptotic decay of the Ising correlations above $T_c$, while the study of the Bose gas density matrix leads us to generalize the Fisher-Hartwig formula to the asymptotic form of random matrix averages over the classical groups and the Gaussian and Laguerre unitary matrix ensembles. Another viewpoint of our generalizations is that they extend to Hankel determinants the Fisher-Hartwig asymptotic form known for Toeplitz determinants.Comment: 25 page

The FERRUM project: Transition probabilities for forbidden lines in [FeII] and experimental metastable lifetimes

Accurate transition probabilities for forbidden lines are important diagnostic parameters for low-density astrophysical plasmas. In this paper we present experimental atomic data for forbidden [FeII] transitions that are observed as strong features in astrophysical spectra. Aims: To measure lifetimes for the 3d^6(^3G)4s a ^4G_{11/2} and 3d^6(^3D)4s b ^4D_{1/2} metastable levels in FeII and experimental transition probabilities for the forbidden transitions 3d^7 a ^4F_{7/2,9/2}- 3d^6(^3G)4s a ^4G_{11/2}. Methods: The lifetimes were measured at the ion storage ring facility CRYRING using a laser probing technique. Astrophysical branching fractions were obtained from spectra of Eta Carinae, obtained with the Space Telescope Imaging Spectrograph onboard the Hubble Space Telescope. The lifetimes and branching fractions were combined to yield absolute transition probabilities. Results: The lifetimes of the a ^4G_{11/2} and the b ^4D_{1/2} levels have been measured and have the following values, 0.75(10) s and 0.54(3) s respectively. Furthermore, we have determined the transition probabilities for two forbidden transitions of a ^4F_{7/2,9/2}- a ^4G_{11/2} at 4243.97 and 4346.85 A. Both the lifetimes and the transition probabilities are compared to calculated values in the literature.Comment: 5 pages, accepted for publication in A&

Random matrix ensembles with an effective extensive external charge

Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two such ensembles have been encounted: an ensemble of unitary matrices specified by the so-called Poisson kernel, and the Laguerre ensemble of positive definite matrices. Here we consider various properties of these ensembles. Jack polynomial theory is used to prove a reproducing property of the Poisson kernel, and a certain unimodular mapping is used to demonstrate that the variance of a linear statistic is the same as in the Dyson circular ensemble. For the Laguerre ensemble, the scaled global density is calculated exactly for all even values of the parameter $\beta$, while for $\beta = 2$ (random matrices with unitary symmetry), the neighbourhood of the smallest eigenvalue is shown to be in the soft edge universality class.Comment: LaTeX209, 17 page

KPZ equation in one dimension and line ensembles

For suitably discretized versions of the Kardar-Parisi-Zhang equation in one space dimension exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through which such results are obtained, namely the method of line ensembles with purely entropic repulsion.Comment: Proceedings STATPHYS22, Bangalore, 200

Parking and the visual perception of space

Using measured data we demonstrate that there is an amazing correspondence among the statistical properties of spacings between parked cars and the distances between birds perching on a power line. We show that this observation is easily explained by the fact that birds and human use the same mechanism of distance estimation. We give a simple mathematical model of this phenomenon and prove its validity using measured data

Live-cell topology assessment of URG7, MRP6₁₀₂ and SP-C using glycosylatable green fluorescent protein in mammalian cells.

Experimental tools to determine membrane topology of a protein are rather limited in higher eukaryotic organisms. Here, we report the use of glycosylatable GFP (gGFP) as a sensitive and versatile membranetopology reporter in mammalian cells. gGFP selectively loses its fluorescence upon N-linked glycosylationin the ER lumen. Thus, positive fluorescence signal assigns location of gGFP to the cytosol whereas nofluorescence signal and a glycosylated status of gGFP map the location of gGFP to the ER lumen. By usingmammalian gGFP, the membrane topology of disease-associated membrane proteins, URG7, MRP6102,SP-C(Val) and SP-C(Leu) was confirmed. URG7 is partially targeted to the ER, and inserted in Cinform.MRP6102and SP-C(Leu/Val) are inserted into the membrane in Coutform. A minor population of untarget-ed SP-C is removed by proteasome dependent quality control system