Universal scaling relations in molecular superconductors

Scaling relations between the superconducting transition temperature $T_{\rm c}$, the superfluid stiffness $\rho_{\rm s}$ and the normal state conductivity $\sigma_0(T_{\rm c})$ are identified within the class of molecular superconductors. These new scaling properties hold as $T_{\rm c}$ varies over two orders of magnitude for materials with differing dimensionality and contrasting molecular structure, and are dramatically different from the equivalent scaling properties observed within the family of cuprate superconductors. These scaling relations place strong constraints on theories for molecular superconductivity.Comment: 4 pages, 4 figure

Quantum Topological Excitations: from the Sawtooth Lattice to the Heisenberg Chain

The recently elucidated structure of the delafossite YCuO$_{2.5}$ reveals a Cu-O network with nearly independent $\Delta$ chains having different interactions between the $s=1/2$ spins. Motivated by this result, we study the $\Delta$ chain for various ratios $J_{\rm bb}/J_{\rm bv}$ of the base-base and base-vertex interactions. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum, which (within numerical error) is the same for total spins $S_{\rm tot}=0$ and 1, has a gap only in the interval $0.4874(1) \leq J_{\rm bb}/J_{\rm bv} \leq 1.53(1)$. The gap is dispersionless for $J_{\rm bb}/J_{\rm bv}=1$, but has increasing $k$-dependence as $J_{\rm bb}/J_{\rm bv}$ moves away from unity, related to the instability of dimers in the ground state.Comment: 4 pages, 6 figures (revtex twocolumn

Multiwavelength study of Cygnus A IV. Proper motion and location of the nucleus

Context. Cygnus A, as the nearest powerful FR II radio galaxy, plays an important role in understanding jets and their impact on the surrounding intracluster medium. Aims. To explain why the nucleus is observed superposed onto the eastern lobe rather than in between the two lobes, and why the jet and counterjet are non-colinear. Methods. We made a comparative study of the radio images at different frequencies of Cygnus A, in combination with the published results on the radial velocities in the Cygnus A cluster. Results. From the morphology of the inner lobes we conclude that the lobes are not interacting with one another, but are well separated, even at low radio frequencies. We explain the location of the nucleus as the result of the proper motion of the galaxy through the cluster. The required proper motion is of the same order of magnitude as the radial velocity offset of Cygnus A with the sub-cluster it belongs to. The proper motion of the galaxy through the cluster likely also explains the non-co-linearity of the jet and counterjet.Comment: Accepted for publication in A&A, 8 pages, 4 figure

Finite Temperature Behavior of Small Silicon and Tin Clusters: An Ab Initio Molecular Dynamics Study

The finite temperature behavior of small Silicon (Si$_{10}$, Si$_{15}$, and Si$_{20}$) and Tin (Sn$_{10}$ and Sn$_{20}$) clusters is studied using isokinetic Born-Oppenheimer molecular dynamics. The lowest equilibrium structures of all the clusters are built upon a highly stable tricapped trigonal prism unit which is seen to play a crucial role in the finite temperature behavior of these clusters. Thermodynamics of small tin clusters (Sn$_{10}$ and Sn$_{20}$) is revisited in light of the recent experiments on tin clusters of sizes 18-21 [G. A. Breaux et. al. Phys. Rev. B {\bf 71} 073410 (2005)]. We have calculated heat capacities using multiple histogram technique for Si$_{10}$, Sn$_{10}$ and Si$_{15}$ clusters. Our calculated specific heat curves have a main peak around 2300 K and 2200 K for Si$_{10}$ and Sn$_{10}$ clusters respectively. However, various other melting indicators such as root mean square bond length fluctuations, mean square displacements show that diffusive motion of atoms within the cluster begins around 650 K. The finite temperature behavior of Si$_{10}$ and Sn$_{10}$ is dominated by isomerization and it is rather difficult to discern the temperature range for transition region. On the other hand, Si$_{15}$ does show a liquid like behavior over a short temperature range followed by the fragmentation observed around 1800 K. Finite temperature behavior of Si$_{20}$ and Sn$_{20}$ show that these clusters do not melt but fragment around 1200 K and 650 K respectively.Comment: 9 figure

The radio luminosity function of radio-loud quasars from the 7C Redshift Survey

We present a complete sample of 24 radio-loud quasars (RLQs) from the new 7C Redshift Survey. Every quasar with a low-frequency (151 MHz) radio flux-density S_151 > 0.5 Jy in two regions of the sky covering 0.013 sr is included; 23 of these have sufficient extended flux to meet the selection criteria, 18 of these have steep radio spectra (hereafter denoted as SSQs). The key advantage of this sample over most samples of RLQs is the lack of an optical magnitude limit. By combining the 7C and 3CRR samples, we have investigated the properties of RLQs as a function of redshift z and radio luminosity L_151. We derive the radio luminosity function (RLF) of RLQs and find that the data are well fitted by a single power-law with slope alpha_1=1.9. We find that there must be a break in the RLQ RLF at log_10(L_151 / W Hz^-1 sr^-1) < 27, in order for the models to be consistent with the 7C and 6C source counts. The z-dependence of the RLF follows a one-tailed gaussian which peaks at z=1.7. We find no evidence for a decline in the co-moving space density of RLQs at higher redshifts. A positive correlation between the radio and optical luminosities of SSQs is observed, confirming a result of Serjeant et al. (1998). We are able to rule out this correlation being due to selection effects or biases in our combined sample. The radio-optical correlation and best-fit model RLF enable us to estimate the distribution of optical magnitudes of quasars in samples selected at low radio frequencies. We conclude that for samples with S_151 < 1 Jy one must use optical data significantly deeper than the POSS-I limit (R approx 20), in order to avoid severe incompleteness.Comment: 28 pages with 13 figures. To appear in MNRA

Field-theory calculation of the electric dipole moment of the neutron and paramagnetic atoms

Electric dipole moments (edms) of bound states that arise from the constituents having edms are studied with field-theoretic techniques. The systems treated are the neutron and a set of paramagnetic atoms. In the latter case it is well known that the atomic edm differs greatly from the electron edm when the internal electric fields of the atom are taken into account. In the nonrelativistic limit these fields lead to a complete suppression, but for heavy atoms large enhancement factors are present. A general bound-state field theory approach applicable to both the neutron and paramagnetic atoms is set up. It is applied first to the neutron, treating the quarks as moving freely in a confining spherical well. It is shown that the effect of internal electric fields is small in this case. The atomic problem is then revisited using field-theory techniques in place of the usual Hamiltonian methods, and the atomic enhancement factor is shown to be consistent with previous calculations. Possible application of bound-state techniques to other sources of the neutron edm is discussed.Comment: 21 pages, 5 figure

The effects of entry on incumbent innovation and productivity

How does firm entry affect innovation incentives and productivity growth in incumbent firms? Micro-data suggests that there is heterogeneity across industries--incumbents in technologically advanced industries react positively to foreign firm entry, but not in laggard industries. To explain this pattern, we introduce entry into a Schumpeterian growth model with multiple sectors which differ by their distance to the technological frontier. We show that technologically advanced entry threat spurs innovation incentives in sectors close to the technological frontier--successful innovation allows incumbents to prevent entry. In laggard sectors it discourages innovation--increased entry threat reduces incumbents' expected rents from innovating. We find that the empirical patterns hold using rich micro-level productivity growth and patent panel data for the UK, and controlling for the endogeneity of entry by exploiting the large number of policy reforms undertaken during the Thatcher era