Is it possible to observe experimentally a metal-insulator transition in ultra cold atoms?

Kicked rotors with certain non-analytic potentials avoid dynamical localization and undergo a metal-insulator transition. We show that typical properties of this transition are still present as the non-analyticity is progressively smoothed out provided that the smoothing is less than a certain limiting value. We have identified a smoothing dependent time scale such that full dynamical localization is absent and the quantum momentum distribution develops power-law tails with anomalous decay exponents as in the case of a conductor at the metal-insulator transition. We discuss under what conditions these findings may be verified experimentally by using ultra cold atoms techniques. It is found that ultra-cold atoms can indeed be utilized for the experimental investigation of the metal-insulator transition.Comment: 7 pages, 3 figure

Modeling Heterogeneous Materials via Two-Point Correlation Functions: II. Algorithmic Details and Applications

In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media) via two-point correlation functions S2 and introduced an efficient heterogeneous-medium (re)construction algorithm called the "lattice-point" algorithm. Here we discuss the algorithmic details of the lattice-point procedure and an algorithm modification using surface optimization to further speed up the (re)construction process. The importance of the error tolerance, which indicates to what accuracy the media are (re)constructed, is also emphasized and discussed. We apply the algorithm to generate three-dimensional digitized realizations of a Fontainebleau sandstone and a boron carbide/aluminum composite from the two- dimensional tomographic images of their slices through the materials. To ascertain whether the information contained in S2 is sufficient to capture the salient structural features, we compute the two-point cluster functions of the media, which are superior signatures of the micro-structure because they incorporate the connectedness information. We also study the reconstruction of a binary laser-speckle pattern in two dimensions, in which the algorithm fails to reproduce the pattern accurately. We conclude that in general reconstructions using S2 only work well for heterogeneous materials with single-scale structures. However, two-point information via S2 is not sufficient to accurately model multi-scale media. Moreover, we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two-point correlation functions.Comment: 35 pages, 19 figure

Influences of Friends and Friendships on Adjustment to Junior High School

To explore influences of friends and friendships on adjustment to junior high school, 101 students were interviewed about their friendships in the spring of sixth grade and again in the fall and spring of seventh grade. Adjustment was judged from self-reports, peer nominations, teacher ratings, and school records. Sociability and leadership increased across the transition if students had high-quality friendships in 6th grade that were mostly stable across the transition. Behavior problems increased if students had stable friendships with sixth-grade friends high in behavioral problems. Sensitivity-isolation of students with sensitive-isolated friends increased across the transition unless they had high-quality, stable friendships. Separate and interactive effects of friendships and friends\u27 characteristics were discussed

Entropy on Spin Factors

Recently it has been demonstrated that the Shannon entropy or the von Neuman entropy are the only entropy functions that generate a local Bregman divergences as long as the state space has rank 3 or higher. In this paper we will study the properties of Bregman divergences for convex bodies of rank 2. The two most important convex bodies of rank 2 can be identified with the bit and the qubit. We demonstrate that if a convex body of rank 2 has a Bregman divergence that satisfies sufficiency then the convex body is spectral and if the Bregman divergence is monotone then the convex body has the shape of a ball. A ball can be represented as the state space of a spin factor, which is the most simple type of Jordan algebra. We also study the existence of recovery maps for Bregman divergences on spin factors. In general the convex bodies of rank 2 appear as faces of state spaces of higher rank. Therefore our results give strong restrictions on which convex bodies could be the state space of a physical system with a well-behaved entropy function.Comment: 30 pages, 6 figure

Magnetization of carbon-coated ferromagnetic nanoclusters determined by electron holography

The magnetic properties of carbon-coated Co and Ni nanoparticles aligned in chains were determined using transmission electron holography. The measurements of the phase change of the electron wave due to the magnetization of the sample were performed. The ratio of remnant magnetization to bulk saturation magnetization Mr/Ms of Co decreased from 53% to 16% and of Ni decreased from 70% to 30% as the particle diameter increased from 25 to 90 nm. It was evident that the inhomogenous magnetic configurations could diminish the stray field of the particles. After being exposed to a 2-Tesla external magnetic field, the Mr/Ms of Co increased by 45% from the original values with the same dependency on the particle size. The Mr/Ms of Ni particles, on the other hand, increased only 10%. The increased magnetization could be attributed to the merging of small domains into larger ones after the exposure to the external magnetic field. The validity of the interpretation of the holograms was established by simulatio

Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles

Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex microstructures, which also make it difficult to model the materials. In this first part of a series of two papers, we collect the known necessary conditions on the standard two-point correlation function S2(r) and formulate a new conjecture. In particular, we argue that given a complete two-point correlation function space, S2(r) of any statistically homogeneous material can be expressed through a map on a selected set of bases of the function space. We provide new examples of realizable two-point correlation functions and suggest a set of analytical basis functions. Moreover, we devise an efficient and isotropy- preserving construction algorithm, namely, the Lattice-Point algorithm to generate realizations of materials from their two- point correlation functions based on the Yeong-Torquato technique. Subsequent analysis can be performed on the generated images to obtain desired macroscopic properties. These developments are integrated here into a general scheme that enables one to model and categorize heterogeneous materials via two-point correlation functions.Comment: 37 pages, 26 figure