Friedel oscillation in charge profile and position dependent screening around a superconducting vortex core

We calculate microscopically the charge distribution around a vortex in type II superconductors by solving the Bogoliubov-de Gennes equation and the Poisson equation simultaneously. Our calculations show that the charge density depletion occurs in the vortex center and the Friedel oscillation appears over the coherence length when k(F)xi is small. We also calculate the density-density correlation function K(r,r(')) as a function of two spatial variables, r and r('), and find that K(r,r(')) is strongly dependent on the distance from the vortex center. We clarify the spatial dependent screening properties on the basis of the correlation function in the core region.     

Intermolecular overlap geometry gives two classes of fulleride superconductor: electronic structure of 38 K Tc Cs3C60

Superconductivity emerges for the A15 polymorph of the fulleride Cs3C60 upon compression to a pressure of approximately 4 kbar. Using density functional theory we study the bonding in the A15 phase as a function of unit cell volume comparing it to that in the fcc polymorph. We find that, despite its smaller packing density, the bcc-derived A15 phase has both a substantially wider bandwidth for the partially occupied t1u band and a higher density of states at the Fermi level. This result can be traced to the striking differences in the nature of the interanion Tc--the two sphere packings (body centered versus face centered) observed experimentally produce two electronically distinct classes of fulleride superconductors.     

Anderson localization of Bogolyubov quasiparticles in interacting Bose-Einstein condensates

We study the Anderson localization of Bogolyubov quasiparticles in an interacting Bose-Einstein condensate (with a healing [corrected] length xi) subjected to a random potential (with a finite correlation length sigma(R)). We derive analytically the Lyapunov exponent as a function of the quasiparticle momentum k, and we study the localization maximum k(max). For 1D speckle potentials, we find that k(max) proportional variant 1/xi when xi>sigma(R) while k(max) proportional variant 1/sigma(R) when xi相似文献   

Dense and nearly jammed random packings of freely jointed chains of tangent hard spheres

Dense packings of freely jointed chains of tangent hard spheres are produced by a novel Monte Carlo method. Within statistical uncertainty, chains reach a maximally random jammed (MRJ) state at the same volume fraction as packings of single hard spheres. A structural analysis shows that as the MRJ state is approached (i) the radial distribution function for chains remains distinct from but approaches that of single hard sphere packings quite closely, (ii) chains undergo progressive collapse, and (iii) a small but increasing fraction of sites possess highly ordered first coordination shells.     

Entropy and temperature of a static granular assembly: an ab initio approach

We construct a statistical framework for static assemblies of deformable grains which parallels that of equilibrium statistical mechanics but with a conservation principle based on the mechanical stress tensor. We define a state function that has all the attributes of entropy. In particular, maximizing this function leads to a well-defined granular temperature and the equivalent of the Boltzman distribution for ensembles of grain packings. Predictions of the ensemble are verified against simulated packings of frictionless, deformable disks.     

Numerical study of the stress response of two-dimensional dense granular packings

We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.     

Experiments on random packings of ellipsoids

Recent simulations indicate that ellipsoids can pack randomly more densely than spheres and, remarkably, for axes ratios near 1.25:1:0.8 can approach the densest crystal packing (fcc) of spheres, with a packing fraction of 74%. We demonstrate that such dense packings are realizable. We introduce a novel way of determining packing density for a finite sample that minimizes surface effects. We have fabricated ellipsoids and show that, in a sphere, the radial packing fraction phi(r) can be obtained from V(h), the volume of added fluid to fill the sphere to height h. We also obtain phi(r) from a magnetic resonance imaging scan. The measurements of the overall density phi(avr), phi(r) and the core density phi(0) = 0.74 +/- 0.005 agree with simulations.     

Scale-free networks are ultrasmall

We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) proportional, variant k(-lambda), i.e., the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small-world networks, which is known to be d approximately ln(N, we show, using analytical arguments, that scale-free networks with 23, d approximately ln(N. We also show that, for any lambda>2, one can construct a deterministic scale-free network with d approximately ln(ln(N, which is the lowest possible diameter.     

Dense packing in the monodisperse hard-sphere system: A numerical study

We report a numerical study of the close packing of monodisperse hard spheres. The close packings of hard spheres are produced by the Lubachesky-Stillinger (LS) compression algorithm and span the range from the disordered states to the ordered states. We provide quantitative evidence for the claim that the density and structural order of the arrested close packing can be determined by the compression rate, i.e., with slower rates producing denser and more ordered structures. Through deeply analyzing the structure of the resulting arrested close packings, a transition region has been identified in the plane of density and reciprocal compression rate, in between what have been historically thought of as amorphous and crystalline packings. We also find clear system size dependences in studying the structural properties of the packings from the disordered ones to the ordered ones. These detailed investigations, on the structure of the arrested close packings, may provide a link between the glassy states and the crystalline states in the hard spheres.     

5- and 6-pulse electron spin echo envelope modulation (ESEEM) of multi-nuclear spin systems

In 3-pulse ESEEM and the original 4-pulse HYSCORE, nuclei with large modulation depth (k approximately 1) suppress spectral peaks from nuclei with weak modulations (k approximately 0). This cross suppression can impede the detection of the latter nuclei, which are often the ones of interest. We show that two extended pulse sequences, 5-pulse ESEEM and 6-pulse HYSCORE, can be used as experimental alternatives that suffer less strongly from the cross suppression and allow to recover signals of k approximately 0 nuclei in the presence of k approximately 1 nuclei. In the extended sequences, modulations from k approximately 0 nuclei are strongly enhanced. In addition, multi-quantum transitions are absent which simplifies the spectra. General analytical expressions for the modulation signals in these sequences are derived and discussed. Numerical simulations and experimental spectra that demonstrate the higher sensitivity of the extended pulse sequences are presented.     

Jamming III: Characterizing randomness via the entropy of jammed matter

The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble of jammed matter and this is shown to be difficult to calculate analytically. A mesoscopic ensemble of isostatic states is then utilized in an effort to predict the entropy through the definition of a volume function that is dependent on the coordination number. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter, and elucidating the phase diagram for jammed granular matter. Analytical calculations are compared to numerical simulations using volume fluctuation analysis and graph theoretical methods, with reasonable agreement. The entropy of the jammed system reveals that random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits. Ensemble calculations show that the entropy vanishes at random close packing (RCP), while numerical simulations show that a finite entropy remains in the microscopic states at RCP. The notion of a negative compactivity, which explores states with volume fractions below those achievable by existing simulation protocols, is also explored, expanding the equations of state. The mesoscopic theory reproduces the simulations results in shape well, though a difference in magnitude implies that the entire entropy of the packing may not be captured by the methods presented herein. We discuss possible extensions to the present mesoscopic approach describing packings from random loose packing (RLP) to RCP to the ordered branch of the equation of state in an effort to understand the entropy of jammed matter in the full range of densities from RLP to face-centered cubic (FCC) packing.     

Wave localization in complex networks with high clustering

We show that strong clustering of links in complex networks, i.e., a high probability of triadic closure, can induce a localization-delocalization quantum phase transition (Anderson-like transition) of coherent excitations. For example, the propagation of light wave packets between two distant nodes of an optical network (composed of fibers and beam splitters) will be absent if the fraction of closed triangles exceeds a certain threshold. We suggest that such an experiment is feasible with current optics technology. We determine the corresponding phase diagram as a function of clustering coefficient and disorder for scale-free networks of different degree distributions P(k) approximately k;{-lambda}. Without disorder, we observe no phase transition for lambda<4, a quantum transition for lambda>4, and an additional distinct classical transition for lambda>4.5. Disorder reduces the critical clustering coefficient such that phase transitions occur for smaller lambda.     

Accuracy and scaling phenomena in Internet mapping

It was recently argued that sampling a network by traversing it with paths from a small number of sources, as with traceroutes on the Internet, creates a fundamental bias in observed topological features like the degree distribution. We examine this bias analytically and experimentally. For Erdo s-Re nyi random graphs with mean degree c, we show analytically that such sampling gives an observed degree distribution P(k) approximately k(-1) for k less, similarc, despite the underlying distribution being Poissonian. For graphs whose degree distributions have power-law tails P(k) approximately k(-alpha), sampling can significantly underestimate alpha when the graph has a large excess (i.e., many more edges than vertices). We find that in order to accurately estimate alpha, one must use a number of sources which grows linearly in the mean degree of the underlying graph. Finally, we comment on the accuracy of the published values of alpha for the Internet.     

A method for calculating the space-time metric inside a collapsing or expanding sphere

A class of solutions of Einstein's field equations is found in which the quantities can be expressed as power series in r. Using null coordinates it is shown that the spacetime metric inside a spherically symmetric distribution of matter can be calculated to any degree of accuracy by evaluating the terms in the power series step by step, provided we know the central density, _O,as a function of time, and the equation of state in the form p=f(), f() being a function analytic at _O.The method is found to be applicable to all cases met with in nature.Presented at the International Conference on Gravitation and Relativity, Copenhagen, July 1971.     

Quantum critical behavior near a density-wave instability in an isotropic fermi liquid

We study the quantum critical behavior in an isotropic Fermi liquid in the vicinity of a zero-temperature density-wave transition at a finite wave vector qc. We show that, near the transition, the Landau damping of the soft bosonic mode yields a crossover in the fermionic self-energy from Sigma(k,omega) approximately Sigma(k) to Sigma(k,omega) approximately Sigma(omega), where k and omega are momentum and frequency. Because of this self-generated locality, the fermionic effective mass diverges right at the quantum critical point, not before; i.e., the Fermi liquid survives up to the critical point.     

Multifractal analysis of Brownian zero set

We present a method for the derivation of the generating function and computation of critical exponents for several cluster models (staircase, bar-graph, and directed column-convex polygons, as well as partially directed self-avoiding walks), starting with nonlinear functional equations for the generating function. By linearizing these equations, we first give a derivation of the generating functions. The nonlinear equations are further used to compute the thermodynamic critical exponents via a formal perturbation ansatz. Alternatively, taking the continuum limit leads to nonlinear differential equations, from which one can extract the scaling function. We find that all the above models are in the same universality class with exponents _u =-1/2, _i =-1/3, and =2/3. All models have as their scaling function the logarithmic derivative of the Airy function.     

Jamming and crystallization in athermal polymer packings

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.     

Observation of coherent sheared turbulence flows in the DIII-D Tokamak

Time-resolved measurements of the turbulent density flow field in a tokamak plasma reveal low-frequency ( approximately 15 KHz), coherent oscillations in the poloidal flow, v(theta). These flow oscillations have a long poloidal wavelength (m<3) and narrow radial extent (k(r)rho(i) approximately 0.2). The estimated flow-shearing rate is of the same order of magnitude as the turbulence decorrelation rate and may thus regulate the turbulence amplitude. These features are consistent with theoretically predicted axisymmetric, self-regulating, sheared flows recognized as geodesic acoustic modes.