Combinatorics and geometry of finite and infinite squaregraphs

Squaregraphs were originally defined as finite plane graphs in which all inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e., the vertices not incident with the outer face) have degrees larger than three. The planar dual of a finite squaregraph is determined by a triangle-free chord diagram of the unit disk, which could alternatively be viewed as a triangle-free line arrangement in the hyperbolic plane. This representation carries over to infinite plane graphs with finite vertex degrees in which the balls are finite squaregraphs. Algebraically, finite squaregraphs are median graphs for which the duals are finite circular split systems. Hence squaregraphs are at the crosspoint of two dualities, an algebraic and a geometric one, and thus lend themselves to several combinatorial interpretations and structural characterizations. With these and the 5-colorability theorem for circle graphs at hand, we prove that every squaregraph can be isometrically embedded into the Cartesian product of five trees. This embedding result can also be extended to the infinite case without reference to an embedding in the plane and without any cardinality restriction when formulated for median graphs free of cubes and further finite obstructions. Further, we exhibit a class of squaregraphs that can be embedded into the product of three trees and we characterize those squaregraphs that are embeddable into the product of just two trees. Finally, finite squaregraphs enjoy a number of algorithmic features that do not extend to arbitrary median graphs. For instance, we show that median-generating sets of finite squaregraphs can be computed in polynomial time, whereas, not unexpectedly, the corresponding problem for median graphs turns out to be NP-hard.Comment: 46 pages, 14 figure

Bose-Einstein condensates on tilted lattices: coherent, chaotic and subdiffusive dynamics

The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein condensate in a tilted optical lattice is studied in a discrete mean-field approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation. If the static field is varied the system shows a plethora of dynamical phenomena. In the strong field limit we demonstrate the existence of (almost) non-spreading states which remain localized on the lattice region populated initially and show coherent Bloch oscillations with fractional revivals in the momentum space (so called quantum carpets). With decreasing field, the dynamics becomes irregular, however, still confined in configuration space. For even weaker fields we find sub-diffusive dynamics with a wave-packet width spreading as $t^{1/4}$.Comment: 4 pages, 5 figure

A Stability Diagram for Dense Suspensions of Model Colloidal Al2O3-Particles in Shear Flow

In Al2O3 suspensions, depending on the experimental conditions very different microstructures can be found, comprising fluid like suspensions, a repulsive structure, and a clustered microstructure. For technical processing in ceramics, the knowledge of the microstructure is of importance, since it essentially determines the stability of a workpiece to be produced. To enlighten this topic, we investigate these suspensions under shear by means of simulations. We observe cluster formation on two different length scales: the distance of nearest neighbors and on the length scale of the system size. We find that the clustering behavior does not depend on the length scale of observation. If inter-particle interactions are not attractive the particles form layers in the shear flow. The results are summarized in a stability diagram.Comment: 15 pages, 10 figures, revised versio

Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance

Assuming the validity of random matrices for describing the statistics of a closed chaotic quantum system, we study analytically some statistical properties of the S-matrix characterizing scattering in its open counterpart. In the first part of the paper we attempt to expose systematically ideas underlying the so-called stochastic (Heidelberg) approach to chaotic quantum scattering. Then we concentrate on systems with broken time-reversal invariance coupled to continua via M open channels. By using the supersymmetry method we derive: (i) an explicit expression for the density of S-matrix poles (resonances) in the complex energy plane (ii) an explicit expression for the parametric correlation function of densities of eigenphases of the S-matrix. We use it to find the distribution of derivatives of these eigenphases with respect to the energy ("partial delay times" ) as well as with respect to an arbitrary external parameter.Comment: 51 pages, RevTEX , three figures are available on request. To be published in the special issue of the Journal of Mathematical Physic

Statistics of S-matrix poles for chaotic systems with broken time reversal invariance: a conjecture

In the framework of a random matrix description of chaotic quantum scattering the positions of $S-$matrix poles are given by complex eigenvalues $Z_i$ of an effective non-Hermitian random-matrix Hamiltonian. We put forward a conjecture on statistics of $Z_i$ for systems with broken time-reversal invariance and verify that it allows to reproduce statistical characteristics of Wigner time delays known from independent calculations. We analyze the ensuing two-point statistical measures as e.g. spectral form factor and the number variance. In addition we find the density of complex eigenvalues of real asymmetric matrices generalizing the recent result by Efetov\cite{Efnh}.Comment: 4 page

The Number Density Evolution of Extreme Emission Line Galaxies in 3D-HST: Results from a Novel Automated Line Search Technique for Slitless Spectroscopy

The multiplexing capability of slitless spectroscopy is a powerful asset in creating large spectroscopic datasets, but issues such as spectral confusion make the interpretation of the data challenging. Here we present a new method to search for emission lines in the slitless spectroscopic data from the 3D-HST survey utilizing the Wide-Field Camera 3 on board the Hubble Space Telescope. Using a novel statistical technique, we can detect compact (extended) emission lines at 90% completeness down to fluxes of 1.5 (3.0) times 10^{-17} erg/s/cm^2, close to the noise level of the grism exposures, for objects detected in the deep ancillary photometric data. Unlike previous methods, the Bayesian nature allows for probabilistic line identifications, namely redshift estimates, based on secondary emission line detections and/or photometric redshift priors. As a first application, we measure the comoving number density of Extreme Emission Line Galaxies (restframe [O III] 5007 equivalent widths in excess of 500 Angstroms). We find that these galaxies are nearly 10 times more common above z~1.5 than at z<0.5. With upcoming large grism surveys such as Euclid and WFIRST as well as grisms featuring prominently on the NIRISS and NIRCam instruments on James Webb Space Telescope, methods like the one presented here will be crucial for constructing emission line redshift catalogs in an automated and well-understood manner.Comment: 16 pages, 14 Figures; Accepted to Ap

Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics

By using the method of orthogonal polynomials we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from Hermitian matrices characterized by the Wigner- Dyson statistics of real eigenvalues to strongly non-Hermitian ones whose complex eigenvalues were studied by Ginibre. Two-point statistical measures (as e.g. spectral form factor, number variance and small distance behavior of the nearest neighbor distance distribution $p(s)$) are studied in more detail. In particular, we found that the latter function may exhibit unusual behavior $p(s)\propto s^{5/2}$ for some parameter values.Comment: 4 pages, RevTE

GAPS IN THE HEISENBERG-ISING MODEL

We report on the closing of gaps in the ground state of the critical Heisenberg-Ising chain at momentum $\pi$. For half-filling, the gap closes at special values of the anisotropy $\Delta= \cos(\pi/Q)$, $Q$ integer. We explain this behavior with the help of the Bethe Ansatz and show that the gap scales as a power of the system size with variable exponent depending on $\Delta$. We use a finite-size analysis to calculate this exponent in the critical region, supplemented by perturbation theory at $\Delta\sim 0$. For rational $1/r$ fillings, the gap is shown to be closed for {\em all} values of $\Delta$ and the corresponding perturbation expansion in $\Delta$ shows a remarkable cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques

Trisodium Dicalcium Bismuth Hexaoxide

Single crystals of the title compound, Na3Ca2BiO6, were grown from a high-temperature reactive flux solution of Na2CO3. Na3Ca2BiO6 crystallizes as an ordered rock-salt structure (space group Fddd), in which the octahedral holes in the oxide array are filled by an ordered 3:2:1 arrangement of Na+, Ca2+ and Bi5+ cations. All atoms except for one O atom lie on special positions; site symmetries are as follows: Bi 222, Ca 2, Na 222 and 2, O 2

Gravito-electromagnetism versus electromagnetism

The paper contains a discussion of the properties of the gravito-magnetic interaction in non stationary conditions. A direct deduction of the equivalent of Faraday-Henry law is given. A comparison is made between the gravito-magnetic and the electro-magnetic induction, and it is shown that there is no Meissner-like effect for superfluids in the field of massive spinning bodies. The impossibility of stationary motions in directions not along the lines of the gravito-magnetic field is found. Finally the results are discussed in relation with the behavior of superconductors.Comment: 13 Pages, LaTeX, 1 EPS figure, to appear in European Journal of Physic