Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class

We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the MF exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence for conformal invariance at the 2D spin-orbit MIT. The presence of boundaries modifies the MF of the whole sample even in the thermodynamic limit.Comment: 5 pages, 4 figure

On the determination of age and mass functions of stars in young open star clusters from the analysis of their luminosity functions

Based on the CCD observations of remote young open clusters NGC 2383, NGC 2384, NGC 4103, NGC 4755, NGC 7510 and Hogg 15, we constructed their observed luminosity functions (LFs). The observed LFs are corrected for field star contamination determined with the help of galactic star count model. In the case of Hogg 15 and NGC 2383 we also considered the additional contamination from neighbouring clusters NGC 4609 and NGC 2384 respectively. These corrections provided the realistic pattern of cluster LF in the vicinity of the MS turn on point and at fainter magnitudes, revealed the so called H-feature arising due to transition of the Pre-MS phase to MS, which is dependent on the cluster age. The theoretical LFs were constructed representing a cluster population model with continuous star formation for a short time scale and a power law Initial Mass Function (IMF) and these were fitted to the observed LF. As a result we are able to determine for each cluster a set of parameters, describing cluster population (the age, duration of star formation, IMF slope and percentage of field star contamination). It was found that in spite of the non-monotonic behaviour of observed LFs, cluster IMFs can be described as the power law functions with slopes similar to Salpeter's value. The present MS turn on cluster ages are several times lower than those derived from the fitting of theoretical isochrones to the turn off region of the upper Main Sequences.Comment: 17 pages, 5 figures, To appear in MNRA

Surface criticality and multifractality at localization transitions

We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at a LD transition is different from that in the bulk. We illustrate this point with a calculation of boundary critical and multifractal behavior at the 2D spin quantum Hall transition and in a 2D metal at scales below the localization length.Comment: Published versio

Boundary multifractality in critical 1D systems with long-range hopping

Boundary multifractality of electronic wave functions is studied analytically and numerically for the power-law random banded matrix (PRBM) model, describing a critical one-dimensional system with long-range hopping. The peculiarity of the Anderson localization transition in this model is the existence of a line of fixed points describing the critical system in the bulk. We demonstrate that the boundary critical theory of the PRBM model is not uniquely determined by the bulk properties. Instead, the boundary criticality is controlled by an additional parameter characterizing the hopping amplitudes of particles reflected by the boundary.Comment: 7 pages, 4 figures, some typos correcte

Entanglement entropy and multifractality at localization transitions

The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the non-analyticity of this entropy at disorder-dominated quantum phase transitions in non-interacting electronic systems. At these critical points, the von Neumann entropy is determined by the single particle wave function intensity which exhibits complex scale invariant fluctuations. We find that the concept of multifractality is naturally suited for studying von Neumann entropy of the critical wave functions. Our numerical simulations of the three dimensional Anderson localization transition and the integer quantum Hall plateau transition show that the entanglement at these transitions is well described using multifractal analysis.Comment: v3, 5 pages, published versio

A complete photometric study of the open cluster NGC 7790 containing Cepheid variables

CCD photometry of the northern open star cluster NGC 7790 has been carried out in BVI photometric passbands down to 21 mag for 1150 stars of which for 700 stars, the data is obtained for the first time. We derive the most reliable parameters for this cluster using all the available photometric, spectroscopic and proper motion data. The interstellar extinction over the cluster area is uniform and normal with E(B-V)=0.5±0.03 mag. We determine a distance of 3.3±0.23 Kpc to the cluster. The theoretical isochrone fittings to the Cepheid variables as well as the evolved part of the main-sequence near turn-off point indicate that the cluster is 120±20 Myr old. We estimate the cluster radius to be 3' 7 using radial stellar density profile. Both the distance and age determined using period luminosity/age relations for the Cepheid variables are consistent with their membership of the cluster. This unique opportunity has therefore been used to refine the zero-point of the period-luminosity relation for the Galactic Cepheids

Boundary criticality and multifractality at the 2D spin quantum Hall transition

Multifractal scaling of critical wave functions at a disorder-driven (Anderson) localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using the supersymmetry technique for disorder averaging. Upon mapping of the spin quantum Hall transition to the classical percolation problem with reflecting boundaries, a number of multifractal exponents governing wave function scaling near a boundary are obtained exactly. Moreover, additional exact boundary scaling exponents of the localization problem are extracted, and the problem is analyzed in other geometries.Comment: v2, 17 pages, 10 figures, published versio