Universal Behavior of Correlations between Eigenvalues of Random Matrices

The universal connected correlations proposed recently between eigenvalues of unitary random matrices is examined numerically. We perform an ensemble average by the Monte Carlo sampling. Although density of eigenvalues and a bare correlation of the eigenvalues are not universal, the connected correlation shows a universal behavior after smoothing.Comment: ISSP-September-199

Breakdown of Universality in Random Matrix Models

We calculate smoothed correlators for a large random matrix model with a potential containing products of two traces \tr W_1(M) \cdot \tr W_2(M) in addition to a single trace \tr V(M). Connected correlation function of density eigenvalues receives corrections besides the universal part derived by Brezin and Zee and it is no longer universal in a strong sense.Comment: 16 pages, LaTex, references and footnote adde

Correlations between eigenvalues of large random matrices with independent entries

We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization group (RG) inspired approach. With the diagrammatic method we obtain a general form for the one, two and three-point connected Green function for this class of ensembles when matrix elements are identically distributed, and then discuss the derivation of higher order functions by the same approach. Using the RG approach we re-derive the one and two-point Green functions and show they are unchanged by choosing certain ensembles with non-identically distributed elements. Throughout, we compare the Green functions we obtain to those from the class of ensembles with unitary invariant distributions and discuss universality in both ensemble classes.Comment: 23 pages, RevTex, hard figures available from [email protected]

Correlation functions of eigenvalues of multi-matrix models, and the limit of a time dependent matrix

We consider the correlation functions of eigenvalues of a unidimensional chain of large random hermitian matrices. An asymptotic expression of the orthogonal polynomials allows to find new results for the correlations of eigenvalues of different matrices of the chain. Eventually, we consider the limit of the infinite chain of matrices, which can be interpreted as a time dependent one-matrix model, and give the correlation functions of eigenvalues at different times.Comment: Tex-Harvmac, 27 pages, submitted to Journ. Phys.

High Resolution Intravital Imaging of Subcellular Structures of Mouse Abdominal Organs Using a Microstage Device

Intravital imaging of brain and bone marrow cells in the skull with subcellular resolution has revolutionized neurobiology, immunology and hematology. However, the application of this powerful technology in studies of abdominal organs has long been impeded by organ motion caused by breathing and heartbeat. Here we describe for the first time a simple device designated ‘microstage’ that effectively reduces organ motions without causing tissue lesions. Combining this microstage device with an upright intravital laser scanning microscope equipped with a unique stick-type objective lens, the system enables subcellular-level imaging of abdominal organs in live mice. We demonstrate that this technique allows for the quantitative analysis of subcellular structures and gene expressions in cells, the tracking of intracellular processes in real-time as well as three-dimensional image construction in the pancreas and liver of the live mouse. As the aforementioned analyses based on subcellular imaging could be extended to other intraperitoneal organs, the technique should offer great potential for investigation of physiological and disease-specific events of abdominal organs. The microstage approach adds an exciting new technique to the in vivo imaging toolbox

A study on the sharp knee and fine structures of cosmic ray spectra

The paper investigates the overall and detailed features of cosmic ray (CR) spectra in the knee region using the scenario of nuclei-photon interactions around the acceleration sources. Young supernova remnants can be the physical realities of such kind of CR acceleration sites. The results show that the model can well explain the following problems simultaneously with one set of source parameters: the knee of CR spectra and the sharpness of the knee, the detailed irregular structures of CR spectra, the so-called "component B" of Galactic CRs, and the electron/positron excesses reported by recent observations. The coherent explanation serves as evidence that at least a portion of CRs might be accelerated at the sources similar to young supernova remnants, and one set of source parameters indicates that this portion mainly comes from standard sources or from a single source.Comment: 13 pages, 4 figures, accepted for publication in SCIENCE CHINA Physics, Mechanics & Astronomy