The temperature dependence of the local tunnelling conductance in cuprate superconductors with competing AF order

Based on the $t-t'-U-V$ model with proper chosen parameters for describing the cuprate superconductors, it is found that near the optimal doping at low temperature ($T$), only the pure d-wave superconductivity ($d$SC) prevails and the antiferromagnetic (AF) order is completely suppressed. At higher $T$, the AF order with stripe modulation and the accompanying charge order may emerge, and they could exist above the $d$SC transition temperature. We calculate the local differential tunnelling conductance (LDTC) from the local density of states (LDOS) and show that their energy variations are rather different from each other as $T$ increases. Although the calculated modulation periodicity in the LDTC/LDOS and bias energy dependence of the Fourier amplitude of LDTC in the "pseudogap" region are in good agreement with the recent STM experiment [Vershinin $et al.$, Science {\bf 303}, 1995 (2004)], we point out that some of the energy dependent features in the LDTC do not represent the intrinsic characteristics of the sample

Effective Low-Energy Model for f-Electron Delocalization

We consider a Periodic Anderson Model (PAM) with a momentum-dependent inter-band hybridization that is strongly suppressed near the Fermi level. Under these conditions, we reduce the PAM to an effective low-energy Hamiltonian, $H_{\rm eff}$, by expanding in the small parameter $V_0/t$ ( $V_0$ is the maximum inter-band hybridization amplitude and $t$ is the hopping integral of the broad band). The resulting model consists of a t-J f-band coupled via the Kondo exchange to the electrons in the broad band. $H_{\rm eff}$ allows for studying the f-electron delocalization transition. The result is a doping-induced Mott transition for the f-electron delocalization, which we demonstrate by density-matrix renormalization group (DMRG) calculations

Post-Oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems

We investigate the orbit-crossing time (T_c) of protoplanet systems both with and without a gas-disk background. The protoplanets are initially with equal masses and separation (EMS systems) scaled by their mutual Hill's radii. In a gas-free environment, we find log (T_c/yr) = A+B \log (k_0/2.3). Through a simple analytical approach, we demonstrate that the evolution of the velocity dispersion in an EMS system follows a random walk. The stochastic nature of random-walk diffusion leads to (i) an increasing average eccentricity ~ t^1/2, where t is the time; (ii) Rayleigh-distributed eccentricities (P(e,t)=e/\sigma^2 \exp(-e^2/(2\sigma^2)) of the protoplanets; (iii) a power-law dependence of T_c on planetary separation. As evidence for the chaotic diffusion, the observed eccentricities of known extra solar planets can be approximated by a Rayleigh distribution. We evaluate the isolation masses of the embryos, which determine the probability of gas giant formation, as a function of the dust and gas surface densities.Comment: 15 pages, 13 figures (2 color ones), accepted for publication in Ap

Bilateral symmetry of object silhouettes under perspective projection

Symmetry is an important property of objects and is exhibited in different forms e.g., bilateral, rotational, etc. This paper presents an algorithm for computing the bilateral symmetry of silhouettes of shallow objects under perspective distortion, exploiting the invariance of the cross ratio to projective transformations. The basic idea is to use the cross ratio to compute a number of midpoints of cross sections and then fit a straight line through them. The goodness-of-fit determines the likelihood of the line to be the axis of symmetry. We analytically estimate the midpoint’s location as a function of the vanishing point for a given object silhouette. Hence finding the symmetry axis amounts to a 2D search in the space of vanishing points. We present experiments on two datasets as well as internet images of symmetric objects that validate our approach. under perspectivities, we analytically compute a set of midpoints of the object as a function of the vanishing point. Then, we fit a straight line passing through the midpoints. The goodness-of-fit defines the likelihood of this line to be a symmetry axis. Using the proposed method, searching for the symmetry axis is reduced to searching for a vanishing point. Our approach is global in the sense that we consider the whole silhouette of the object rather than small parts of it. The results show that the method presented here is capable of finding axes of symmetry of considerably distorted perspective images. 2 Related Work

Interacting Individuals Leading to Zipf's Law

We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statisticsComment: 4 pages 2 figure

Fermi gas in harmonic oscillator potentials

Assuming the validity of grand canonical statistics, we study the properties of a spin-polarized Fermi gas in harmonic traps. Universal forms of Fermi temperature $T_F$, internal energy $U$ and the specific heat per particle of the trapped Fermi gas are calculated as a {\it function} of particle number, and the results compared with those of infinite number particles.Comment: 8 pages, 1 figure, LATE

The momentum distribution of J/psi in B decays

The discrepancy between theory and data in the momentum distribution of slow J/psi in B decays has been several times addressed as a puzzle. Using the most recent results on exclusive B decays into J/psi and heavy kaons or exotic mesons and reconsidering the non-relativistic-QCD calculation of the color octet fragmentation component, we show that an improvement in the comparison between data and theory can be obtained. There is still room for a better fit to data and this may imply that new exotic mesons of the XYZ kind have yet to be discovered.Comment: 4 pages, 2 figures, 2 tables. To appear in Physical Review

Chemical evolution of star clusters

I discuss the chemical evolution of star clusters, with emphasis on old globular clusters, in relation to their formation histories. Globular clusters clearly formed in a complex fashion, under markedly different conditions from any younger clusters presently known. Those special conditions must be linked to the early formation epoch of the Galaxy and must not have occurred since. While a link to the formation of globular clusters in dwarf galaxies has been suggested, present-day dwarf galaxies are not representative of the gravitational potential wells within which the globular clusters formed. Instead, a formation deep within the proto-Galaxy or within dark-matter minihaloes might be favoured. Not all globular clusters may have formed and evolved similarly. In particular, we may need to distinguish Galactic halo from Galactic bulge clusters.Comment: 27 pages, 2 figures. To appear as invited review article in a special issue of the Phil. Trans. Royal Soc. A: Ch. 6 "Star clusters as tracers of galactic star-formation histories" (ed. R. de Grijs). Fully peer reviewed. LaTeX, requires rspublic.cls style fil