Statistical properties of random density matrices

Statistical properties of ensembles of random density matrices are investigated. We compute traces and von Neumann entropies averaged over ensembles of random density matrices distributed according to the Bures measure. The eigenvalues of the random density matrices are analyzed: we derive the eigenvalue distribution for the Bures ensemble which is shown to be broader then the quarter--circle distribution characteristic of the Hilbert--Schmidt ensemble. For measures induced by partial tracing over the environment we compute exactly the two-point eigenvalue correlation function.Comment: 8 revtex pages with one eps file included, ver. 2 - minor misprints correcte

Inference of kinetic Ising model on sparse graphs

Based on dynamical cavity method, we propose an approach to the inference of kinetic Ising model, which asks to reconstruct couplings and external fields from given time-dependent output of original system. Our approach gives an exact result on tree graphs and a good approximation on sparse graphs, it can be seen as an extension of Belief Propagation inference of static Ising model to kinetic Ising model. While existing mean field methods to the kinetic Ising inference e.g., na\" ive mean-field, TAP equation and simply mean-field, use approximations which calculate magnetizations and correlations at time $t$ from statistics of data at time $t-1$, dynamical cavity method can use statistics of data at times earlier than $t-1$ to capture more correlations at different time steps. Extensive numerical experiments show that our inference method is superior to existing mean-field approaches on diluted networks.Comment: 9 pages, 3 figures, comments are welcom

Integrable theory of quantum transport in chaotic cavities

The problem of quantum transport in chaotic cavities with broken time-reversal symmetry is shown to be completely integrable in the universal limit. This observation is utilised to determine the cumulants and the distribution function of conductance for a cavity with ideal leads supporting an arbitrary number $n$ of propagating modes. Expressed in terms of solutions to the fifth Painlev\'e transcendent and/or the Toda lattice equation, the conductance distribution is further analysed in the large-$n$ limit that reveals long exponential tails in the otherwise Gaussian curve.Comment: 4 pages; final version to appear in Physical Review Letter

500 TeV gamma rays from Hercules X-1

A signal (chance probability = .0002) with the 1.24 s period of Hercules X-1 has been observed using the Utah Fly's Eye. The signal's relatively long period and high shower energy conflict with some popular models of particle acceleration by pulsars. Optical and X-ray data suggest a picture in which energetic particles produce multi-TeV gamma rays by collisions with Hercules X-1's accretion disk

All sky Northern Hemisphere 10(15) EV gamma-ray survey

Flux limits in the range 10 to the minus 13th power-10 to the minus 12 power/sq cm/s have been obtained by observing Cerenkov flashes from small air showers. During 1983, a 3.5 sigma excess of showers was observed during the phase interval 0.2 to 0.3 of the 4.8h period of Cygnus X-3, but no excess was found in 1984 observations

Skew-orthogonal Laguerre polynomials for chiral real asymmetric random matrices

We apply the method of skew-orthogonal polynomials (SOP) in the complex plane to asymmetric random matrices with real elements, belonging to two different classes. Explicit integral representations valid for arbitrary weight functions are derived for the SOP and for their Cauchy transforms, given as expectation values of traces and determinants or their inverses, respectively. Our proof uses the fact that the joint probability distribution function for all combinations of real eigenvalues and complex conjugate eigenvalue pairs can be written as a product. Examples for the SOP are given in terms of Laguerre polynomials for the chiral ensemble (also called the non-Hermitian real Wishart-Laguerre ensemble), both without and with the insertion of characteristic polynomials. Such characteristic polynomials play the role of mass terms in applications to complex Dirac spectra in field theory. In addition, for the elliptic real Ginibre ensemble we recover the SOP of Forrester and Nagao in terms of Hermite polynomials

Sources and Secondary Production of Organic Aerosols in the Northeastern United States during WINTER

Most intensive field studies investigating aerosols have been conducted in summer, and thus, wintertime aerosol sources and chemistry are comparatively poorly understood. An aerosol mass spectrometer was flown on the National Science Foundation/National Center for Atmospheric Research C‐130 during the Wintertime INvestigation of Transport, Emissions, and Reactivity (WINTER) 2015 campaign in the northeast United States. The fraction of boundary layer submicron aerosol that was organic aerosol (OA) was about a factor of 2 smaller than during a 2011 summertime study in a similar region. However, the OA measured in WINTER was almost as oxidized as OA measured in several other studies in warmer months of the year. Fifty‐eight percent of the OA was oxygenated (secondary), and 42% was primary (POA). Biomass burning OA (likely from residential heating) was ubiquitous and accounted for 33% of the OA mass. Using nonvolatile POA, one of two default secondary OA (SOA) formulations in GEOS‐Chem (v10‐01) shows very large underpredictions of SOA and O/C (5×) and overprediction of POA (2×). We strongly recommend against using that formulation in future studies. Semivolatile POA, an alternative default in GEOS‐Chem, or a simplified parameterization (SIMPLE) were closer to the observations, although still with substantial differences. A case study of urban outflow from metropolitan New York City showed a consistent amount and normalized rate of added OA mass (due to SOA formation) compared to summer studies, although proceeding more slowly due to lower OH concentrations. A box model and SIMPLE perform similarly for WINTER as for Los Angeles, with an underprediction at ages \u3c6 hr, suggesting that fast chemistry might be missing from the models