The Gelfand map and symmetric products

If A is an algebra of functions on X, there are many cases when X can be regarded as included in Hom(A,C) as the set of ring homomorphisms. In this paper the corresponding results for the symmetric products of X are introduced. It is shown that the symmetric product Sym^n(X) is included in Hom(A,C) as the set of those functions that satisfy equations generalising f(xy)=f(x)f(y). These equations are related to formulae introduced by Frobenius and, for the relevant A, they characterise linear maps on A that are the sum of ring homomorphisms. The main theorem is proved using an identity satisfied by partitions of finite sets.Comment: 14 pages, Late

Numerical Calculation of the Fidelity for the Kondo and the Friedel-Anderson Impurities

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N_{eff} of states. A plot of ln(F) versus N\proptoln(N_{eff}) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F)-ln(N_{eff}) plot for the Kondo impurity diverges for large N_{eff}. On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N_{eff} when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime. PACS: 75.20.Hr, 71.23.An, 71.27.+a, 05.30.-

Lagrangian approach to a symplectic formalism for singular systems

We develop a Lagrangian approach for constructing a symplectic structure for singular systems. It gives a simple and unified framework for understanding the origin of the pathologies that appear in the Dirac-Bergmann formalism, and offers a more general approach for a symplectic formalism, even when there is no Hamiltonian in a canonical sense. We can thus overcome the usual limitations of the canonical quantization, and perform an algebraically consistent quantization for a more general set of Lagrangian systems.Comment: 30 page

Oscillations of the magnetic polarization in a Kondo impurity at finite magnetic fields

The electronic properties of a Kondo impurity are investigated in a magnetic field using linear response theory. The distribution of electrical charge and magnetic polarization are calculated in real space. The (small) magnetic field does not change the charge distribution. However, it unmasks the Kondo cloud. The (equal) weight of the d-electron components with their magnetic moment up and down is shifted and the compensating s-electron clouds don't cancel any longer (a requirement for an experimental detection of the Kondo cloud). In addition to the net magnetic polarization of the conduction electrons an oscillating magnetic polarization with a period of half the Fermi wave length is observed. However, this oscillating magnetic polarization does not show the long range behavior of Rudermann-Kittel-Kasuya-Yosida oscillations because the oscillations don't extend beyond the Kondo radius. They represent an internal electronic structure of the Kondo impurity in a magnetic field. PACS: 75.20.Hr, 71.23.An, 71.27.+

The Eliashberg Function of Amorphous Metals

A connection is proposed between the anomalous thermal transport properties of amorphous solids and the low-frequency behavior of the Eliashberg function. By means of a model calculation we show that the size and frequency dependence of the phonon mean-free-path that has been extracted from measurements of the thermal conductivity in amorphous solids leads to a sizeable linear region in the Eliashberg function at small frequencies. Quantitative comparison with recent experiments gives very good agreement.Comment: 4pp., REVTeX, 1 uuencoded ps fig. Original posting had a corrupted raw ps fig appended. Published as PRB 51, 689 (1995

Coulomb and quantum oscillator problems in conical spaces with arbitrary dimensions

The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic oscillator eigenfunctions is performed through the introduction of non-local ladder operators. By exploiting the hidden symmetry of the two-dimensional harmonic oscillator the eigenvalues for the angular momentum operators in three dimensions are reproduced. A generalization for N-dimensions is performed for both Coulomb and harmonic oscillator problems in angular deficit space-times. It is thus established the connection among the states and energies of both problems in these topologically non-trivial space-times.Comment: 15 page

Severe discrepancies between experiment and theory in the superconducting proximity effect

The superconducting proximity effect is investigated for SN double layers in a regime where the resulting transition temperature T_{c} does not depend on the mean free paths of the films and, within limits, not on the transparency of the interface. This regime includes the thin film limit and the normalized initial slope S_{sn}= (d_{s}/T_{s})|dT_{c}/dd_{n}|. The experimental results for T_{c} are compared with a numerical simulation which was recently developed in our group. The results for the SN double layers can be devided into three groups: (i) When N = Cu, Ag, Au, Mg a disagreement between experiment and theory by a factor of the order of three is observed, (ii) When N = Cd, Zn, Al the disagreement between experiment and theory is reduced to a factor of about 1.5, (iii) When N = In, Sn a reasonably good agreement between experiment and theory is observed

A Compact Approximate Solution to the Friedel-Anderson Impuriy Problem

An approximate groundstate of the Anderson-Friedel impurity problem is presented in a very compact form. It requires solely the optimization of two localized electron states and consists of four Slater states (Slater determinants). The resulting singlet ground state energy lies far below the Anderson mean field solution and agrees well with the numerical results by Gunnarsson and Schoenhammer, who used an extensive 1/N_{f}-expansion for a spin 1/2 impurity with double occupancy of the impurity level. PACS: 85.20.Hr, 72.15.R

Gemini NIFS survey of feeding and feedback processes in nearby Active Galaxies: I - Stellar kinematics

We use the Gemini Near-Infrared Integral Field Spectrograph (NIFS) to map the stellar kinematics of the inner few hundred parsecs of a sample of 16 nearby Seyfert galaxies, at a spatial resolution of tens of parsecs and spectral resolution of 40 km/s. We find that the line-of-sight (LOS) velocity fields for most galaxies are well reproduced by rotating disk models. The kinematic position angle (PA) derived for the LOS velocity field is consistent with the large scale photometric PA. The residual velocities are correlated with the hard X-ray luminosity, suggesting that more luminous AGN have a larger impact in the surrounding stellar dynamics. The central velocity dispersion values are usually higher than the rotation velocity amplitude, what we attribute to the strong contribution of bulge kinematics in these inner regions. For 50% of the galaxies, we find an inverse correlation between the velocities and the $h_3$ Gauss-Hermitte moment, implying red wings in the blueshifted side and blue wings in the redshifted side of the velocity field, attributed to the movement of the bulge stars lagging the rotation. Two of the 16 galaxies (NGC 5899 and Mrk 1066) show an S-shape zero velocity line, attributed to the gravitational potential of a nuclear bar. Velocity dispersion maps show rings of low-$\sigma$ values (50-80 km/s) for 4 objects and "patches" of low-sigma for 6 galaxies at 150-250 pc from the nucleus, attributed to young/ intermediate age stellar populations.Comment: To be published in MNRA

Gossip on Weighted Networks

We investigate how suitable a weighted network is for gossip spreading. The proposed model is based on the gossip spreading model introduced by Lind et.al. on unweighted networks. Weight represents "friendship." Potential spreader prefers not to spread if the victim of gossip is a "close friend". Gossip spreading is related to the triangles and cascades of triangles. It gives more insight about the structure of a network. We analyze gossip spreading on real weighted networks of human interactions. 6 co-occurrence and 7 social pattern networks are investigated. Gossip propagation is found to be a good parameter to distinguish co-occurrence and social pattern networks. As a comparison some miscellaneous networks and computer generated networks based on ER, BA, WS models are also investigated. They are found to be quite different than the human interaction networks.Comment: 8 pages, 4 figures, 1 tabl