Real-Space Renormalization Group (RSRG) Approach to Quantum Spin Lattice Systems

The paper describes an explicit variational modification of the standard RSRG method and its application to quantum spin lattice systems. The modified approach is applied to exactly solvable ITF, XX and isotropic Heisenberg models. Better upper bounds for the systems' ground state energy are obtained as compared to the standard RSRG approach.Comment: http://www.mff.cuni.cz/veda/konference/wds/proc/proc-contents.php?year=2011#phy

Relationship between the Elemental Abundances and the Kinematics of Galactic-Field RR Lyrae Stars

Data of our compiled catalog containing the positions, velocities, and metallicities of 415 RR~Lyrae variable stars and the relative abundances [el/Fe] of 12~elements for 101 RR~Lyrae stars, including four $\alpha$~elements (Mg, Ca, Si, and Ti), are used to study the relationships between the chemical and spatial--kinematic properties of these stars. In general, the dependences of the relative abundances of $\alpha$~elements on metallicity and velocity for the RR~Lyrae stars are approximately the same as those for field dwarfs. Despite the usual claim that these stars are old, among them are representatives of the thin disk, which is the youngest subsystem of the Galaxy. Attention is called to the problem of low-metallicity RR~Lyrae stars. Most RR~Lyrae stars that have the kinematic properties of thick disk stars have metallicities ${\rm [Fe/H]} < -1.0$ and high ratios [$\alpha$/Fe]$\approx 0.4$, whereas only about 10\,\% of field dwarfs belonging to the so-called "low-metallicity tail" have this chemical composition. At the same time, there is a sharp change in [$\alpha$/Fe] in RR~Lyrae stars belonging just to the thick disk, providing evidence for a long period of formation of this subsystem. The chemical compositions of SDSS J1707+58, V455 Oph, MACHO 176.18833.411, V456 Ser, and BPS CS 30339--046 do not correspond to their kinematics. While the first three of these stars belong to the halo, according to their kinematics, the last two belong to the thick disk. It is proposed that they are all most likely extragalactic, but the possible appearance of some of them in the solar neighborhood as a result of the gravitational action of the bar on field stars cannot be ruled out.Comment: 16 pages, 3 figures, 1 tabl

The Chemical Composition of Globular Clusters of Different Nature in our Galaxy

A catalog of Galactic globular clusters has been compiled and used to analyze relations between the chemical and kinematic parameters of the clusters. The catalog contains positions, distances, luminosities, metallicites, and horizontal-branch morphology indices for 157~globular clusters, as well as space velocities for 72~globular clusters. For 69~globular clusters, these data are suppleented with the relative abundances of 28~chemical elements produced in various nuclear-synthesis processes, taken from 101~papers published between 1986 and 2018. The tendency for redder horizontal branches in low-metallicity accreted globular clusters is discussed. The discrepancy between the criteria for cluster membership in the thick-disk and halo subsystems based on chemical and kinematic properties is considered. This is manifest through the fact that all metal-rich ($\rm{[Fe/H]} > -1.0$) clusters are located close to the center and plane of the Galaxy, regardless of their kinematic membership in particular Galaxy subsystems. An exception is three accreted clusters lost by a dwarf galaxy in Sagittarius. At the same time, the fraction of more distant clusters is high among metal-poorer clusters in any kinematically selected Galactic subsystem.Comment: 21 pages, 4 figures, 2 table

Destruction of the phase coherence by the magnetic field in the fluctuation region of thin superconducting film

It was shown as long ago as 1998 cond-mat/9811051 that the vortex lattice melting theories are science fiction because the Abrikosov state is not the vortex lattice with crystalline long-range order. Nevertheless this false conception is used up to now in many works including the lecture notes cond-mat/0111052 providing a pedagogical introduction. This false conception has resulted from visual but incorrect ideas. In spite of outward appearances only long-range order - long-range phase coherence exists in the Abrikosov state. The phase transition interpreted erroneously as the vortex lattice melting is in reality a disappearance of long-range phase coherence. The investigation of the nonlocal resistivity made in this work is experimental evidence that a state without phase coherence, differed qualitatively from mythical vortex liquid, is observed above this transition.Comment: 4 pages, 3 figure

Peculiarities of {\alpha}-element abundances in Galactic open clusters

A catalog compiling the parameters of 346 open clusters, including their metallicities, positions, ages, and velocities has been composed. The elements of the Galactic orbits for 272 of the clusters have been calculated. Spectroscopic determinations of the relative abundances, [el/Fe], for 14 elements synthesized in various nuclear processes averaged over data from 109 publications are presented for 90 clusters. Since no systematic effects distorting the relative abundances of the studied elements in these clusters have been found, these difference suggest real differences between clusters with high, elongated orbits and field stars. In particular, this supports the earlier conclusion, based on an analysis of the elements of the Galactic orbits, that some clusters formed as a result of interactions between high-velocity, metal-poor clouds and the interstellar medium of the Galactic thin disk. On average, clusterswith high, elongated orbits and metallicities ${\rm [Fe/H]} < - 0.1$ display lower relative abundances of the primary \'a elements than do field stars. The low [O,Mg/Fe] ratios of these clusters can be understood if the high-velocity clouds that gave rise to them were formed of interstellar material from regions where the star-formation rate and/or the masses of Type II supernovae were lower than near the Galactic plane. It is also shown that, on average, the relative abundances of the primary $\alpha$-elements are higher in relatively metal-rich clusters with high, elongated orbits than in field stars. This can be understood if clusters with ${\rm [Fe/H]} > - 0.1$ formed as a result of interactions between metal-rich clouds with intermediate velocities and the interstellar medium of the Galactic disk; such clouds could form from returning gas in a so-called "Galactic fountain".Comment: 23 pages, 5 figures, 2 table

Peculiarities of the abundances of neutron-capture elements in Galactic open clusters

The properties of the relative abundances of rapid and slow neutron-capture elements are studied using a catalog containing spectroscopic abundance determinations for 14~elements produced in various nuclear-synthesis processes for 90~open clusters. The catalog also contains the positions, ages, velocities, and elements of the Galactic orbits of the clusters. The relative abundances of both $r$-elements (Eu) and $s$-elements (Y, Ba, La, and Ce) in clusters with high, elongated orbits and in field stars of the Galactic thin disk display different dependences on metallicity, age, Galactocentric distance, and the elements of the Galactic orbits, supporting the view that these objects have different natures. In young clusters, not only barium, but also the three other studied $s$-elements display significantly higher relative abundances than field stars of the same metallicity. The relative abundances of Eu are lower in high-metallicity clusters (${\rm [Fe/H]} > -0.1$) with high, elongated orbits than in field giants, on average, while the [Eu/Fe] ratios in lower-metallicity clusters are the same as those in field stars, on average, although with a large scatter. The metallicity dependence of the [O, Mg/Eu] ratios in clusters with high, elongated orbits and in field stars are substantially different. These and other described properties of the Eu abundances, together with the properties of the abundances of primary $\alpha$-elements, can be understood in a natural way if clusters with high, elongated orbits with different metallicities formed as a result of interactions of two types of high-velocity clouds with the interstellar medium of the Galactic disk: low-metallicity high-velocity clouds that formed from "primordial" gas, and high-metallicity clouds with intermediate velocities that formed in "Galactic fountains".Comment: 14 pages, 3 figure

Annular Long Josephson Junctions in a Magnetic Field: Engineering and Probing the Fluxon Interaction Potential

The interaction of a Josephson fluxon with an external magnetic field-induced potential in a long Josephson junction is investigated experimentally. The thermal activation of the fluxon from a potential well is observed and experiments probing its predicted quantum properties are discussed. A method for engineering a magnetic double-well potential for a fluxon is proposed and the use of the coupled fluxon states for quantum computation is suggested.Comment: 11 pages, 6 figure

Nonlocal electrodynamics of long ultra-narrow Josephson junctions: Experiment and theory

We experimentally and theoretically investigate electromagnetic cavity modes in ultra-narrow Al-AlO$_x$-Al and Nb-AlO$_x$-Nb long Josephson junctions. Experiments show that the voltage spacing between the Fiske steps on the current-voltage characteristics of sub-$\mu$m wide and several hundred $\mu$m long Al-AlO$_x$-Al and Nb-AlO$_x$-Nb Josephson junctions increases when decreasing the width of a junction. This effect is explained by stray magnetic fields, which become important for narrow junctions. Theoretical estimates of the Fiske step voltage based on a nonlocal wave propagation equation are in good agreement with our experimental data. Using the nonlocal model, we determine the size and mass of a Josephson vortex by means of a variational approach, and relate vortex size to the experimentally measured critical magnetic field of the junction.Comment: Submitted to Phys. Rev.

On the scaling behaviour of the alternating spin chain

In this note we report the results of our study of a 1D integrable spin chain whose critical behaviour is governed by a CFT possessing a continuous spectrum of scaling dimensions. It is argued that the computation of the density of Bethe states of the continuous theory can be reduced to the calculation of the connection coefficients for a certain class of differential equations whose monodromy properties are similar to those of the conventional confluent hypergeometric equation. The finite size corrections to the scaling are also discussed.Comment: 30 pages, 14 figure

Peculiarities of Abundances of Selected Elements in Metal-Rich Field RR Lyrae Stars

We use the data of our extended catalog of spectroscopic determinations of elemental abundances in the atmospheres of Galactic-field RR Lyrae type variables to show that metal-rich RR Lyraes ($\rm{[Fe/H]} > -1.0$) have anomalous abundances of some elements. In particular, the relative abundances of scandium, titanium, and yttrium in metal-rich RR Lyrae type variables are lower than the corresponding abundances in field stars of similar metallicity beyond the errors. We discuss the errors of the determination of the abundances of the above elements and point out the fact that no europium, zirconium, and lanthanum abundance determinations are available for metal-rich RR Lyrae type variables. We also analyze various possible causes of the observed peculiarities of the chemical composition of metal-rich RR Lyrae type variables.Comment: 12 pages, 2 figures, 2 table