The spectral properties of the Falicov-Kimball model in the weak-coupling limit

The $f$ and $d$ electron density of states of the one-dimensional Falicov-Kimball model are studied in the weak-coupling limit by exact diagonalization calculations. The resultant behaviors are used to examine the $d$-electron gap ($\Delta_{d}$), the $f$-electron gap ($\Delta_{f}$), and the $fd$-electron gap ($\Delta_{fd}$) as functions of the $f$-level energy $E_f$ and hybridization $V$. It is shown that the spinless Falicov-Kimball model behaves fully differently for zero and finite hybridization between $f$ and $d$ states. At zero hybridization the energy gaps do not coincide ($\Delta_{d}\neq \Delta_{f} \neq \Delta_{fd}$), and the activation gap $\Delta_{fd}$ vanishes discontinuously at some critical value of the $f$-level energy $E_{fc}$. On the other hand, at finite hybridization all energy gaps coincide and vanish continuously at the insulator-metal transition point $E_f=E_{fc}$. The importance of these results for a description of real materials is discussed.Comment: 10 pages, 7 figures, LaTe

The suppression of superconductivity in MgCNi3 by Ni-site doping

The effects of partial substitution of Cu and Co for Ni in the intermetallic perovskite superconductor MgCNi3 are reported. Calculation of the expected electronic density of states suggests that electron (Cu) and hole (Co) doping should have different effects. For MgCNi3-xCux, solubility of Cu is limited to approximately 3% (x = 0.1), and Tc decreases systematically from 7K to 6K. For MgCNi3-xCox, solubility of Co is much more extensive, but bulk superconductivity disappears for Co doping of 1% (x = 0.03). No signature of long range magnetic ordering is observed in the magnetic susceptibility of the Co doped material.Comment: submitted, Solid State Communication

Von Neumann Regular Cellular Automata

For any group $G$ and any set $A$, a cellular automaton (CA) is a transformation of the configuration space $A^G$ defined via a finite memory set and a local function. Let $\text{CA}(G;A)$ be the monoid of all CA over $A^G$. In this paper, we investigate a generalisation of the inverse of a CA from the semigroup-theoretic perspective. An element $\tau \in \text{CA}(G;A)$ is von Neumann regular (or simply regular) if there exists $\sigma \in \text{CA}(G;A)$ such that $\tau \circ \sigma \circ \tau = \tau$ and $\sigma \circ \tau \circ \sigma = \sigma$, where $\circ$ is the composition of functions. Such an element $\sigma$ is called a generalised inverse of $\tau$. The monoid $\text{CA}(G;A)$ itself is regular if all its elements are regular. We establish that $\text{CA}(G;A)$ is regular if and only if $\vert G \vert = 1$ or $\vert A \vert = 1$, and we characterise all regular elements in $\text{CA}(G;A)$ when $G$ and $A$ are both finite. Furthermore, we study regular linear CA when $A= V$ is a vector space over a field $\mathbb{F}$; in particular, we show that every regular linear CA is invertible when $G$ is torsion-free elementary amenable (e.g. when $G=\mathbb{Z}^d, \ d \in \mathbb{N}$) and $V=\mathbb{F}$, and that every linear CA is regular when $V$ is finite-dimensional and $G$ is locally finite with $\text{Char}(\mathbb{F}) \nmid o(g)$ for all $g \in G$.Comment: 10 pages. Theorem 5 corrected from previous versions, in A. Dennunzio, E. Formenti, L. Manzoni, A.E. Porreca (Eds.): Cellular Automata and Discrete Complex Systems, AUTOMATA 2017, LNCS 10248, pp. 44-55, Springer, 201

Disk evaporation in a planetary nebula

We study the Galactic bulge planetary nebula M 2-29 (for which a 3-year eclipse event of the central star has been attributed to a dust disk) using HST imaging and VLT spectroscopy, both long-slit and integral field. The central cavity of M 2-29 is filled with a decreasing, slow wind. An inner high density core is detected, with radius less than 250 AU, interpreted as a rotating gas/dust disk with a bipolar disk wind. The evaporating disk is argued to be the source of the slow wind. The central star is a source of a very fast wind (1000 km/s). An outer, partial ring is seen in the equatorial plane, expanding at 12 km/s. The azimuthal asymmetry is attributed to mass-loss modulation by an eccentric binary. M 2-29 presents a crucial point in disk evolution, where ionization causes the gas to be lost, leaving a low-mass dust disk behind.Comment: 11 pages, accepted for publication in "Astronomy and Astrophysics

Superconductivity in Geometrically Frustrated Pyrochlore RbOs2O6

We report the basic thermodynamic properties of the new geometrically frustrated beta-pyrochlore bulk superconductor RbOs2O6 with a critical temperature Tc = 6.4 K. Specific heat measurements are performed in magnetic fields up to 12 T. The electronic density of states at the Fermi level in the normal state results in gamma = (33.7 \pm 0.2) mJ/mol_f.u./K^2. In the superconducting state, the specific heat follows conventional BCS-type behavior down to 1 K, i.e. over three orders of magnitude in specific heat data. The upper critical field slope at Tc is 1.2 T/K, corresponding to a Maki-parameter alpha = 0.64 \pm 0.1. From the upper critical field mu0 Hc2 \approx 6 T at 0 K, we estimate a Ginzburg-Landau coherence length xi \approx 7.4 nm. RbOs2O6 is the second reported metallic AB2O6 type pyrochlore compound after KOs2O6, and one of only three pyrochlore superconductors in addition to Cd2Re2O7 and KOs2O6