New Results for Diffusion in Lorentz Lattice Gas Cellular Automata

New calculations to over ten million time steps have revealed a more complex diffusive behavior than previously reported, of a point particle on a square and triangular lattice randomly occupied by mirror or rotator scatterers. For the square lattice fully occupied by mirrors where extended closed particle orbits occur, anomalous diffusion was still found. However, for a not fully occupied lattice the super diffusion, first noticed by Owczarek and Prellberg for a particular concentration, obtains for all concentrations. For the square lattice occupied by rotators and the triangular lattice occupied by mirrors or rotators, an absence of diffusion (trapping) was found for all concentrations, except on critical lines, where anomalous diffusion (extended closed orbits) occurs and hyperscaling holds for all closed orbits with {\em universal} exponents ${\displaystyle{d_f = \frac{7}{4}}}$ and ${\displaystyle{\tau = \frac{15}{7}}}$. Only one point on these critical lines can be related to a corresponding percolation problem. The questions arise therefore whether the other critical points can be mapped onto a new percolation-like problem, and of the dynamical significance of hyperscaling.Comment: 52 pages, including 18 figures on the last 22 pages, email: [email protected]

Single grain heating due to inelastic cotunneling

We study heating effects of a single metallic quantum dot weakly coupled to two leads. The dominant mechanism for heating at low temperatures is due to inelastic electron cotunneling processes. We calculate the grain temperature profile as a function of grain parameters, bias voltage, and time and show that for nanoscale size grains the heating effects are pronounced and easily measurable in experiments.Comment: 4 pages, 3 figures, revtex4, extended and corrected versio

Active Semi-Supervised Learning Using Sampling Theory for Graph Signals

We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured by the edge weights. Given a target number of nodes to label, the goal is to choose those nodes that are most informative and then predict the unknown labels. We propose a novel framework for this problem based on our recent results on sampling theory for graph signals. A graph signal is a real-valued function defined on each node of the graph. A notion of frequency for such signals can be defined using the spectrum of the graph Laplacian matrix. The sampling theory for graph signals aims to extend the traditional Nyquist-Shannon sampling theory by allowing us to identify the class of graph signals that can be reconstructed from their values on a subset of vertices. This approach allows us to define a criterion for active learning based on sampling set selection which aims at maximizing the frequency of the signals that can be reconstructed from their samples on the set. Experiments show the effectiveness of our method.Comment: 10 pages, 6 figures, To appear in KDD'1

Anisotropy Reversal of the Upper Critical Field at Low Temperatures and Spin-Locked Superconductivity in K2Cr3As3

We report the first measurements of the anisotropic upper critical field $H_{c2}(T)$ for K$_{2}$Cr$_{3}$As$_{3}$ single crystals up to 60 T and $T > 0.6$ K. Our results show that the upper critical field parallel to the Cr chains, $H_{c2}^\parallel (T)$, exhibits a paramagnetically-limited behavior, whereas the shape of the $H_{c2}^\perp (T)$ curve (perpendicular to the Cr chains) has no evidence of paramagnetic effects. As a result, the curves $H_{c2}^\perp (T)$ and $H_{c2}^\parallel(T)$ cross at $T\approx 4$ K, so that the anisotropy parameter $\gamma_H(T)=H_{c2}^\perp/H_{c2}^\parallel (T)$ increases from $\gamma_H(T_c)\approx 0.35$ near $T_c$ to $\gamma_H(0)\approx 1.7$ at 0.6 K. This behavior of $H_{c2}^\|(T)$ is inconsistent with triplet superconductivity but suggests a form of singlet superconductivity with the electron spins locked onto the direction of Cr chains

Growth of High-Mobility Bi2Te2Se Nanoplatelets on hBN Sheets by van der Waals Epitaxy

The electrical detection of the surface states of topological insulators is strongly impeded by the interference of bulk conduction, which commonly arises due to pronounced doping associated with the formation of lattice defects. As exemplified by the topological insulator Bi2Te2Se, we show that via van der Waals epitaxial growth on thin hBN substrates the structural quality of such nanoplatelets can be substantially improved. The surface state carrier mobility of nanoplatelets on hBN is increased by a factor of about 3 compared to platelets on conventional Si/SiOx substrates, which enables the observation of well-developed Shubnikov-de Haas oscillations. We furthermore demonstrate the possibility to effectively tune the Fermi level position in the films with the aid of a back gate