Bulletin of the American Physical Society
Joint Fall 2011 Meeting of the Texas Sections of the APS, AAPT, and Zone 13 of the SPS
Volume 56, Number 7
Thursday–Saturday, October 6–8, 2011; Commerce, Texas
Session N1: Foundations of Quantum Systems II |
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Chair: William Newton, Texas A&M University--Commerce Room: Sam Rayburn Center Second Floor, Room Innovations A |
Saturday, October 8, 2011 12:05PM - 12:17PM |
N1.00001: Magnetohydrodynamic Verification Problem and Solution Jared Rovny A new magnetohydrodynamic (MHD) verification test problem has been developed. The problem consists of an infinite conducting cylinder of arbitrary but constant conductivity and uniform magnetic permeability that is rotating at constant angular velocity in an infinite vacuum background. Initially there is a uniform magnetic field everywhere. The two-dimensional time and space dependent solution for the magnetic field in the conductor and the vacuum regions will be discussed. [Preview Abstract] |
Saturday, October 8, 2011 12:17PM - 12:29PM |
N1.00002: Equilibrium Properties of a Particle Hopping on a Lattice: A Path Integral Study Mark O'Callaghan, Bruce Miller We study the equilibrium properties of a single quantum particle (qp) hopping on a one-dimensional lattice. We develop the path-integral formalism in which the quantum particle is represented by a closed variable-step random walk on the lattice. Here we explicitly consider the case of a free particle, which can be directly compared with an analytical solution. We utilize the canonical ensemble and derive expressions for the energy, it's mean square fluctuation, and the qp-qp correlation function in position. One interesting and salient feature of the computation algorithm that shall be stressed is the importance of computing the bins for the probability of a step of a certain size and direction from least probable to most probable, since in this way additions will be performed from very small numbers progressively to larger numbers. If care is not taken in this manner, errant numerical artifacts are introduced simply because of the error associated with addition (subtraction) of very small numbers to (from) much larger numbers. The intention of this paper is to review the derivations of the aforementioned and provide evidence from numerical (Monte Carlo) simulation of the benefits of the algorithm. [Preview Abstract] |
Saturday, October 8, 2011 12:29PM - 12:41PM |
N1.00003: Nonspherical model density matrices for Rung 3.5 exchange-correlation functionals Austin Aguero, Benjamin Janesko Kohn-Sham (KS) density functional theory models electrons' complicated many-body interactions using exchange-correlation density functionals. Semilocal functionals, rungs 1-3 on the ``Jacob's Ladder'' of approximate exchange-correlation functionals, model the XC energy density at each point r using information from an infinitesimal region about r. Nonlocal fourth-rung exchange functionals incorporate a dependence on the entire one-particle density matrix of the noninteracting KS reference system. Nonlocal functionals provide improved accuracy for many properties, but have higher computational costs, particularly in extended systems. ``Rung 3.5'' exchange functionals incorporate the product of the KS density matrix with a semilocal model density matrix, balancing the strengths and limitations of semilocal and nonlocal approximations. This work proposes new semilocal model density matrices for Rung 3.5 functionals. Semilocal density matrices containing 1-3 parameters improve upon previous work for both molecular thermochemistry and kinetics, and show promise for development of future non-empirical Rung 3.5 Density Functionals. [Preview Abstract] |
Saturday, October 8, 2011 12:41PM - 12:53PM |
N1.00004: Dynamical Stability of a One-dimensional Plasma Matthew Roberts, Bruce Miller Since the days of the early computers, computer simulations have been incredibly important to the study of the motion of systems of particles as a way to model such systems as stars in a galaxy or charges in plasmas, which cannot be physically produced in a laboratory. These models are still used today, to the great benefit of the scientific community. In this study, the interaction of a one-dimensional system of charges with periodic boundary conditions is modeled with a computer simulation using an Euler integration technique. The chaos in a particular system is then studied through the computation of the largest Lyapunov exponent for that system. It is revealed that the value for this largest exponent, while independent of the initial conditions for a particular system, is dependent upon the size of the system, i.e. the number of particles in the system, as well as the charge-to-mass ratio of these particles. We will present the results of different computer simulations to demonstrate these dependencies by graphing intermediate averages for the greatest Lyapunov exponents over time for a set of systems of either different sizes, or with different charge-to-mass ratios. [Preview Abstract] |
Saturday, October 8, 2011 12:53PM - 1:05PM |
N1.00005: Studies of Hydrogenic Quantum Systems Using the Feynman-Kac Path Integral Method J.M. Rejcek, N.G. Fazleev The Feynman-Kac path integral method is applied to several hydrogenic quantum systems for the purpose of evaluating eigenvalues of the lowest eigenstates. These are computed by random walk simulations on a discrete grid. The systems studied include free hydrogen, hydrogen and antihydrogen in a confined spherical well. The study provides the latest simulation analysis and includes rescaling and the use of symmetry that allows higher order eigenstates to be computed. The method provides exact values in the limit of infinitesimal step size and infinite time for the lowest eigenstates. [Preview Abstract] |
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