Bulletin of the American Physical Society
2008 APS March Meeting
Volume 53, Number 2
Monday–Friday, March 10–14, 2008; New Orleans, Louisiana
Session S39: Systems Far From Equilibrium and Other Topics in Statistical Physics |
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Sponsoring Units: GSNP Chair: Robert Ziff, University of Michigan Room: Morial Convention Center 231 |
Wednesday, March 12, 2008 2:30PM - 2:42PM |
S39.00001: Absorbing-state phase transitions: exact solutions of small systems Ronald Dickman I derive precise results for absorbing-state phase transitions using exact (numerically determined) quasistationary (QS) probability distributions for small systems. Analysis of the contact process on rings of 23 or fewer sites yields critical properties (control parameter, order-parameter ratios, and critical exponents $z$ and $\beta/\nu_\perp$) with an accuracy of better than 0.1\%; for the exponent $\nu_\perp$ the accuracy is about 0.5\%. Good results are also obtained for the pair contact process. The QS kurtosis exhibits a sharp minimum at the critical point. [Preview Abstract] |
Wednesday, March 12, 2008 2:42PM - 2:54PM |
S39.00002: Displacement and velocity correlation functions of magnetic particle chains undergoing Brownian dynamics Yuk Kwan Ho, Mingjie Zheng, Kin Wah Yu Brownian dynamics of physical systems has been studied for a long time since Einstein in 1905. In this work, we report the study of a magnetic particle chain in ferrofluid, with hydrodynamic interactions and harmonic interactions included, by using Rice method [1]. We will focus on the correlation functions and relaxation time of the chain. As qualitative account for the effect of system parameters, analytic solutions of the displacement and velocity correlation functions of a two-body system have been studied. In the case of an over-damped system, very long relaxation time for the displacement correlation function can be obtained from the analytic solutions. Moreover, the size dependence of the relaxation time is also studied numerically for moderate chain sizes. \newline \newline [1] M. C. Wang and G. E. Uhlenbeck, Rev. Mod. Phys. \textbf{17}, 323 (1945). [Preview Abstract] |
Wednesday, March 12, 2008 2:54PM - 3:06PM |
S39.00003: Theory of Zener tunneling and breakdown in solids Naoyuki Sugimoto, Shigeki Onoda, Naoto Nagaosa Tunneling and breakdown phenomena are among of the most important problems in condensed matter physics. We study the Zener tunneling and breakdown phenomena in a bulk system taking into account the dissipation due to impurity scatterings in terms of the Keldysh formalism. Three distinct regions are recognized for the current-field characteristics, which are identified as the impurity-conduction, the Zener tunneling, and the Zener breakdown, respectively. The crossovers among them are described in a unified fashion. By examining the local density of states, which can be measured by scanning tunneling spectroscopy, we find that the Zener tunneling and breakdown can be understood as the conduction due to the finite local density of states at the Fermi energy originating from the hybridization between the conduction and valence bands induced by the electric field. [Preview Abstract] |
Wednesday, March 12, 2008 3:06PM - 3:18PM |
S39.00004: Domain Structure Universality in Coarsening Benjamin Vollmayr-Lee, Andrew Rutenberg, Sohei Yasuda Coarsening systems ubiquitously exhibit power law growth $L\sim t^\alpha$ with self-similiar domain morphology, and much progress has been made in mapping out universality classes of the growth exponent $\alpha$. It has been commonly argued that these universality classes should apply as well to the scaled domain structure, but recent evidence has appeared to the contrary. In particular, surface tension anisotropy has been found numerically and by exact solutions in the dilute limit to modify the domain morphology and structure factor, while leaving growth exponents unchanged. Thus the universality classes of the domain morphology remains an open question. We present a conjecture that the morpology universality is a consequence of the asymptotic trajectories of the topological defects, and then map out the universality classes that follow. Our prediction, in the case of scalar, conserved order parameter coarsening, is that the domain structures depend on surface tension anisotropy and mobility asymmetry, but nothing more. To test this prediction we have conducted extensive simulations of coarsening with mobility asymmetry and have demonstrated its influence on the scaled domain structure. [Preview Abstract] |
Wednesday, March 12, 2008 3:18PM - 3:30PM |
S39.00005: Exact Solutions for Anisotropic Coarsening in the Dilute Limit William Rosenbaum, Melinda Gildner, Benjamin Vollmayr-Lee We study the influence of anisotropy on coarsening dynamics via two dilute coarsening models: Lifshitz-Slyozov theory for locally conserved order parameter dynamics, and Wagner theory for the globally conserved analog. We adopt a perturbative approach to analyze the effect of surface tension anisotropy on drop shapes and the scaled drop size distribution. In both models we find that coarsening solutions exhibit growth laws that are unchanged from the isotropic theories, $L\sim t^{1/3}$ and $L\sim t^{1/2}$ respectively, and drop shapes that are in general nonspherical and non-Wulffian. We also determine that the drop size distribution varies from the isotropic case. [Preview Abstract] |
Wednesday, March 12, 2008 3:30PM - 3:42PM |
S39.00006: Domain Morphology and Structure Factor in the Asymmetric Cahn-Hilliard Equation Sohei Yasuda, Benjamin Vollmayr-Lee, Andrew Rutenberg The Cahn-Hilliard equation for conserved order parameter coarsening is modified to allow for unequal mobilities in the two equilibrium phases. This asymmetric Cahn-Hilliard equation is then simulated using an unconditionally stable algorithm, which enables reaching times well into the $L\sim t^{1/3}$ dynamic scaling regime. Our goal is to address questions of the universality of the scaled domain morphology; in particular, to test our conjecture that the morphology should depend on the mobility asymmetry. We study mobility ratios of 1, 2, 4 and 8 and find that the domain size distribution depends strongly on the mobility asymmetry: the higher (lower) mobility phase forms a smaller (larger) backbone cluster with more (fewer) smaller domains, and the magnitude of the effect grows with the mobility ratio. Interestingly, the structure factor shows no discernible dependence on the mobility asymmetry. [Preview Abstract] |
Wednesday, March 12, 2008 3:42PM - 3:54PM |
S39.00007: Non-trivial statistics crossover in random sequential adsorption due to the presence of a pattern Nuno A.M. Araujo, Antonio Cadilhe, Vladimir Privman The random sequential adsorption (RSA) on a lattice approaches the jammed state exponentially, while in the off-lattice version approaches the jammed state as a power-law. In this presentation, we focus on the kinetics leading to the jammed state. The presence of pattern influences the kinetics of approach to the jammed state. Namely, a pattern consisting of equal size squares embedded on a square matrix lattice provides a rich set of regimes. Measurements of the distribution of areas available for adsorption during the process make possible to predict how the jammed state is attained: power-law or exponential. Finally, we associate these two different kinetic regimes with the breakdown of Pommeau statistics near the jammed state. [Preview Abstract] |
Wednesday, March 12, 2008 3:54PM - 4:06PM |
S39.00008: Dephasing and the steady state in quantum many-particle systems Thomas Barthel, Ulrich Schollw\"ock We discuss relaxation in many-particle systems. For integrable systems, the time-evolution from an arbitrary initial state can lead, for a given finite subsystem, to a definite steady state. We give an explicit derivation of the steady state ensemble and devise sufficient prerequisites for the dephasing to take place. We also find surprisingly simple scenarios, in which dephasing is ineffective and discuss the dependence on dimensionality and criticality. It also follows that, after a quench of system parameters, entanglement entropy will become extensive. [Preview Abstract] |
Wednesday, March 12, 2008 4:06PM - 4:18PM |
S39.00009: Assembly and control of self-propelled structures in driven suspensions of magnetic microparticles. Maxim Belkin, Alexey Snezhko, Igor Aranson, Wai-Kwong Kwok Magnetic microparticles suspended on the surface of liquid and subjected to periodic vertical magnetic excitations form a non-trivial dynamic snake-like pattern accompanied by large-scale surface flows. Apparently, controlled suppression of vortices at one end of the snake may lead to a formation of a self-propelled structure. We demonstrate that the suppression of the vortex pair can be implemented by the mechanical disturbance of the one end of the structure by means of the floating particle with characteristic size comparable to the width of the snake's segment. The snake structure with the particle attached to its end becomes a swimmer with parameters effectively controlled by the external driving magnetic field. Experimental studies of such self-propelled structures are presented. [Preview Abstract] |
Wednesday, March 12, 2008 4:18PM - 4:30PM |
S39.00010: Avalanches of Bose-Einstein-Condensates from open optical lattices Tsampikos Kottos, Gim Seng Ng, Holger Hennig, Ragnar Fleischmann, Theo Geisel We investigate, the outgoing atomic flux of BECs loaded in large OLs using a mean field (Discrete Non-Linear Schroedinger Equation--DNLSE) approach. We show that for some critical values of the rescaled (with respect to the lattice size) interatomic interaction strength, the current decays in avalanches that follow a power-law distribution indicating the existence of a novel phase transition. The origin of this phenomenon is identified to be the collisions between stable and moving breathers which co-exist at the lattice. Using a reduce map we are able to provide bounds for the power law exponent of the avalanche distribution which reflect the complexity of the underlying classical phase-space. Due to the inter-disciplinary nature of the DNLSE, we expect that the same phenomenon will be observed in several other branches of nonlinear physics, ranging from nonlinear optics to polarons and biological molecules. [Preview Abstract] |
Wednesday, March 12, 2008 4:30PM - 4:42PM |
S39.00011: Study of universality and critical behavior in periodically driven interacting cold atomic system Myoung-Sun Heo, Yonghee Kim, Wonho Jhe, Heung-Ryoul Noh Strongly driven nonlinear oscillators show a variety of interesting phenomena such as period doubling, bifurcation, chaos. Since their resonant behaviors are very sensitive to external perturbation, they have now been widely adopted for the precise determination of physical quantities. The key concept to these researches is the development of bistable or period-2 states, which are, in most cases, energetically degenerate. If particles interact each other, however, this degeneracy of two attractors can be lifted up. For example, in the simple case of all-to-all attractive interaction, particles will be preferably directed into more populated attractors. Being incorporated with random fluctuation which tries to equilibrate population in each attractor, this lifting-up becomes dependent on the system size, or the total number of particles, as recently observed as spontaneous symmetry breaking in cold atomic system which inherently possesses the light-induced attractive interaction. In particular, this dependence seems to show a sort of critical behavior. Here we have elucidated the criticality existing in the strongly driven interacting many-particle system consisted up of cold atoms from static and dynamic perspectives. [Preview Abstract] |
Wednesday, March 12, 2008 4:42PM - 4:54PM |
S39.00012: Transition of Electromechanical Pendulum into Nonlinear Response Chulki Kim, Hua Qin, Hyun-Seok Kim, Robert Blick We present measurements on a macroscopic electron shuttle in the regime of nonlinear response. The shuttle is formed by a classical mechanical pendulum situated between two capacitor plates. The main advantage of this macroscopic setup is that we can directly measure the onset of nonlinear response of this electromechanical pendulum exhibiting period doubling. The results will find use in application such as bifurcation amplifier in nanoscopic versions of the device. A model nanoelectromechanical device based on the macroscopic experiment has the potential to reveal nonlinear quantum mechanical effects. [Preview Abstract] |
Wednesday, March 12, 2008 4:54PM - 5:06PM |
S39.00013: Harmonic measure of DLA and percolation clusters Robert Ziff, Leonard Sander, David Adams The problem of efficiently finding the harmonic measure of DLA and percolation clusters is addressed. Deep inside fjords and inlets of irregular surfaces, traditional methods of solving Laplace's equation become very inefficient. A new numerical algorithm that efficiently solves for those measures is developed. The technique uses a step-by-step approach that adds a shell at each time step to the diffusion front, and is essentially linear in the number of sites considered. The method works for lattice systems and discretized versions of continuum systems. With it, we have solved for the multifractal exponents of the fractal surfaces. For DLA, we address the controversy of the behavior of the harmonic measure deep inside the fjord. For percolation, we consider both the relatively smooth accessible hull (D = 4/3), and the very invaginated regular hull (D = 7/4). [Preview Abstract] |
Wednesday, March 12, 2008 5:06PM - 5:18PM |
S39.00014: Critical surfaces for general two dimensional bond percolation problems Chris Scullard, Robert Ziff We present a general method for deriving approximate bond percolation critical surfaces for general two dimensional lattices. Our approach is to assume that the critical surface is at most first order in its arguments and then to impose symmetries and known special cases until the function is completely determined. We show also that allowing higher powers of the arguments gives increasingly accurate approximations. For the Archimedean lattices the critical thresholds we find by this method are accurate to at least 4 significant figures. In two other cases, the checkerboard and inhomogeneous bow-tie we find critical surfaces that appear, from our numerical investigation, to be exact but that apparently cannot be rigorously derived by any existing technique. The checkerboard formula that we find is same as that conjectured by Wu (Rev. Mod. Phys. 54, 235 - 268 (1982)) [Preview Abstract] |
Wednesday, March 12, 2008 5:18PM - 5:30PM |
S39.00015: Nonuniversal Deviations From Predictions of the Random Matrix Theory of Wave Chaotic Scattering: Theory and Experiment Steven Anlage, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott The eigenfunctions and spectra of chaotic billiards are notoriously sensitive to small perturbations.~ Thus statistical approaches have been developed to model such systems.~ In recent work, we used random matrix theory to develop statistical models for the impedance of a chaotic microwave cavity coupled to a small number of antennas, with the only parameters being the radiation impedance of the antennas, the area of the cavity and a uniform loss parameter Q [S. Hemmady, \textit{et al.}, Phys. Rev. Lett. \textbf{94}, 014102 (2005); X. Zheng, \textit{et al}., Electromagnetics \textbf{26}, 3 (2006)].~ The theory generally agrees well with experiment, but under some circumstances the experimental and numerical results deviate significantly from the Random Matrix Theory predictions.~ We have derived a method of accounting for these deviations and have experimental and numerical results which agree well with our new, non-universal, predictions. [Preview Abstract] |
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