Age Dating of Globular Clusters Using UBV(RI) Main-sequence Photometry in the Two-color Diagram: Age of NGC 6397

I propose and apply a method for deriving ages of the metal-poor globular clusters (GCs) in a distance-independent way, which is based on age indicator related to the main sequence in the two-color diagrams with U-B index. Age of the metal-poor GC NGC 6397 has been estimated, using Yale isochrones of Demarque et al. (1996), to be close to 16 Gyr provided the cluster metallicity is near [Fe/H]=-2.0.Comment: 2 pages, 1 figure, uses IAU207_pasp.sty (included). To be published in the Proceedings of the IAU Symposium 207, "Extragalactic Star Clusters", eds. E.K. Grebel, D. Geisler and D. Minnit

Nonlinear Quantum Coherence Effects in Driven Mesoscopic Systems

In these pedagogical notes the diffuson-cooperon perturbation theory of weak localization and mesoscopic phenomena is extended to describe non-equilibrium and nonlinear effects in quantum disordered systems. It is shown how such perturbation theory works in the time and frequency domain for essentially nonlinear phenomena. Examples of quantum rectification in a mesoscopic ring and the dynamic localization in quantum dots are discussed in detail.Comment: 36 pages, 21 figures, Proceedings of LXXXI Les Houches School on "Nanoscopic quantum transport", Les Houches, France, June 28-July 30, 200

Spectral Statistics at the Anderson Transition: Multifractality of Wave Functions and the Violation of the Normalization Sum Rule

The statistics of energy levels of electrons in a random potential is considered in the critical energy window near the mobility edge. It is shown that the multifractality of critical wave functions results in the violation of the normalization sum rule in the thermodynamic limit and leads to the quasi-Poisson linear term in the level number variance. The slope of the linear term is equal to the sum rule deficiency which is expressed in terms of the fractal dimension D(2).Comment: Proceedings of the Correlated Fermions and Transport in Mesoscopic Systems Moriond Conference, Les Arcs, 1996. 10 pages REVTEX, one figur

Second-Parameter Globular Clusters in the Milky Way and in M33 as Tracers of Mass Loss from M31 in the Early Epoch?

I suggest that the bulk of the "young", second-parameter globular clusters (SPGCs) observed in the outer halo of our Galaxy and recently found in other massive spiral of the Local Group (LG), M33, may have originated due to mass outflow from M31 and subsequent accretion of gas on the Galaxy and M33 in the early epoch.Comment: 2 pages, no figures, uses IAU207_pasp.sty. To be published in the Proceedings of the IAU Symposium 207, "Extragalactic Star Clusters", eds. E.K. Grebel, D. Geisler and D. Minnit

Large-scale distribution of quasars in deep pencil-beam surveys

We have used integral two-point spatial correlation function and its second derivative to analyze the distribution of quasars in three very deep surveys published in the literature. Statistically significant ($\sim 2-3\sigma$) correlations were found at scales of $\sim 50-100h^{-1}$ Mpc in all of the analyzed surveys. We have used the friends-of-friends cluster analysis to show that these correlations can be explained by the presence of relatively small quasar clusters (3-6 objects) which may possibly belong to larger structures such as Large Quasar Groups found in the bigger surveys. The sizes of these clusters along the redshift direction and distances between them are similar to those for structures found recently in studies of CIV absorption systems. These results present further evidence for the existence of large-scale structures at redshifts $z\sim 1-2$.Comment: 5 pages, 2 figures, LaTeX (uses mn.sty), submitted to MNRAS, also available at http://astro.nmsu.edu/~akravtso/publications.htm

Random matrix representations of critical statistics

We consider two random matrix ensembles which are relevant for describing critical spectral statistics in systems with multifractal eigenfunction statistics. One of them is the Gaussian non-invariant ensemble which eigenfunction statistics is multifractal, while the other is the invariant random matrix ensemble with a shallow, log-square confinement potential. We demonstrate a close correspondence between the spectral as well as eigenfuncton statistics of these random matrix ensembles and those of the random tight-binding Hamiltonian in the point of the Anderson localization transition in three dimensions. Finally we present a simple field theory in 1+1 dimensions which reproduces level statistics of both of these random matrix models and the classical Wigner-Dyson spectral statistics in the framework of the unified formalism of Luttinger liquid. We show that the (equal-time) density correlations in both random matrix models correspond to the finite-temperature density correlations of the Luttinger liquid. We show that spectral correlations in the invariant ensemble with log-square confinement correspond to a Luttinger liquid in the 1+1 curved space-time with the event horizon, similar to the phonon density correlations in the sonic analogy of Hawking radiation in black holes.Comment: 21 pages, 4 figures, Chapter in the Handbook on Random Matrix Theor

Self-Induced Formaton of Metal-Rich Globulars in Bulges?

Taken together, key latest observations assume that (i) old metal-rich globular cluster populations (MRGCPs) in bulges were able to form due to essentially increased, self(internally)-induced star formation rate (SFR) in the hosts, while galaxy merging played an additional role; (ii) massive star cluster populations (MSCPs) in irregulars may be young, less prominent counterparts of the old MRGCPs in spheroids.Comment: 1 page, no figures, poster presenrted at JD06, IUA General Assembly, Sydney, July 17, 2003, to appear in Highlights of Astronom

Metal-Rich Globular Clusters: an Unaccounted Factor Responsible for Their Formation?

Presently unaccounted but quite probable "chemical factor" may be responsible for the formation of old metal-rich globular clusters (MRGCs) in spheroids, as well as of their conterparts, young (intermediate-age) massive star clusters (MSCs) in irregulars. Their formation presumably occurs at the same stage of the host galaxies' chemical evolution and is related to the essentially increased SF activity in the hosts around the same metallicity, Zsol/3 ([Fe/H]~-0.5). It is achieved very soon in massive spheroids, later in lower-mass spheroids, and (much) more later in irregulars.Comment: 2 pages, 1 figure; to be published in the proceedings of the conference "Globular Clusters - Guides to Galaxies", held in Concepcion, Chile, March 200

Dephasing and Dynamic Localization in Quantum Dots

The effects of dynamic localization in a solid-state system -- a quantum dot -- are considered. The theory of weak dynamic localization is developed for non-interacting electrons in a closed quantum dot under arbitrary time-dependent perturbation and its equivalence to the theory of weak Anderson localization is demonstrated. The dephasing due to inelastic electron scattering is shown to destroy the dynamic localization in a closed quantum dot leading to the classical energy absorption at times much greater than the inelastic scattering time. Finally a realistic case of a dot weakly connected to leads is studied and it is shown that the dynamic localization may lead to a drastic change of the shape of the Coulomb blockade peak in the dc conductance vs the gate voltage.Comment: 24 pages, 7 figures, Proceeding of the NATO Conference "Fundamental Problems of Mesoscopic Physics: Interaction and Decoherence.", Granada (Spain

Random matrix theory: Wigner-Dyson statistics and beyond. (Lecture notes of a course given at SISSA (Trieste, Italy))

This is a course on Random Matrix Theory which includes traditional as well as advanced topics presented with an extensive use of classical logarithmic plasma analogy and that of the quantum systems of one-dimensional interacting fermions with inverse square interaction (Calogero-Sutherland model). Certain non-invariant random matrix ensembles are also considered with the emphasis on the eigenfunction statistics in them. The course can also be viewed as introduction to theory of localization where the (non-invariant) random matrix ensembles play a role of the toy models to illustrate functional methods based on super-vector/super-matrix representations.Comment: TeX, 27 page