DOCSLIB.ORG

Monopoles and Fractional Vortices in Chiral Superconductors

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Monopoles and Fractional Vortices in Chiral Superconductors Monopoles and fractional vortices in chiral superconductors G. E. Volovik* Low Temperature Laboratory, Helsinki University of Technology, Box 2200, FIN-02015 HUT, Espoo, Finland; and Landau Institute for Theoretical Physics, 117334, Moscow, Russia Communicated by Olli V. Lounasmaa, Helsinki University of Technology, Espoo, Finland, December 22, 1999 (received for review November 24, 1999) I discuss two exotic objects that must be experimentally identified in for the Standard Model (see ref. 5 for a review): the outgoing flux chiral superfluids and superconductors. These are (i) the vortex with of the hypermagnetic field is compensated by the incoming hyper- .(charge flux through the Z-string (Fig. 1 ؍ in chiral superfluids, and N 1͞2 ؍ a fractional quantum number (N in chiral superconductors), which plays the part of the In condensed matter, there are also topological objects that 1͞4 ؍ and N 1͞2 Alice string in relativistic theories and (ii) the hedgehog in the ˆl field, imitate magnetic monopoles. In chiral superconductors, their which is the counterpart of the Dirac magnetic monopole. These structure is very similar to the nexus: it is the magnetic monopole objects of different dimensions are topologically connected. They combined either with two Abrikosov vortices, each carrying the form the combined object that is called a nexus in relativistic theories. ͞ ⌽ flux (1 2) 0, or with four half-quantum vortices, each playing In chiral superconductors, the nexus has magnetic charge emanating the part of 1͞4 of the Dirac string. I also discuss the interaction radially from the hedgehog, whereas the half-quantum vortices play of such topological defects in superconductors with the ‘t the part of the Dirac string. Each half-quantum vortex supplies the Hooft–Polyakov monopole. If the latter exists, then the nexus fractional magnetic flux to the hedgehog, representing 1͞4ofthe provides a natural topological trap for the magnetic monopole. ‘‘conventional’’ Dirac string. I discuss the topological interaction of the superconductor’s nexus with the ‘t Hooft–Polyakov magnetic mono- Symmetry Groups. The similarity between the objects in Standard pole, which can exist in Grand Unified Theories. The monopole and Model and in chiral superconductors stems from the similar the hedgehog with the same magnetic charge are topologically symmetry breaking scheme. In the Standard Model, the local confined by a piece of the Abrikosov vortex. Such confinement makes ϫ the nexus a natural trap for the magnetic monopole. Other properties electroweak symmetry group SU(2)W U(1)Y at high energy is broken at low energy to the diagonal subgroup of the electro- of half-quantum vortices and monopoles are discussed as well, ϭ Ϫ including fermion zero modes. magnetism U(1)Q, where Q Y W3 is the electric charge. In amorphous chiral superconductors, the relevant symmetry above the superconducting transition temperature T is SO(3) ϫ agnetic monopoles do not exist in classical electromagne- c L U(1) , where SO(3) is a global group of the orbital rotations. tism. Maxwell equations show that the magnetic field is Q L M Below T , the symmetry is broken to the diagonal subgroup divergenceless, ٌ⅐B ϭ 0, which implies that the magnetic flux c Ϫ ͛ ⅐ ϭ U(1)Q L3. In high-energy physics, such symmetry breaking of through any closed surface is zero: SdS B 0. If one tries to construct the monopole solution B ϭ gr͞r3, the condition that the global and local groups to the diagonal global subgroup is magnetic field is nondivergent requires that magnetic flux ⌽ϭ called semilocal, and the corresponding topological defects are 4␲g from the monopole must be accompanied by an equal called semilocal strings (5). Thus, in chiral superconductors, the strings are semilocal; however, in electrically neutral chiral singular flux supplied to the monopole by an attached Dirac ϫ string. Quantum electrodynamics, however, can be successfully superfluids, they are global, because both groups in SO(3)L modified to include magnetic monopoles. In 1931, Dirac (1) U(1) are global there. showed that the string emanating from a magnetic monopole If one first neglects the difference between the global and local becomes invisible for electrons if the magnetic flux of the groups, the main difference between the symmetry breaking monopole is quantized in terms of the elementary magnetic flux schemes in high-energy physics and chiral superconductors is the discrete symmetry. It is the difference between SU(2) and hc SO(3) ϭ SU(2)͞Z and also one more discrete symmetry, Z , 4␲g ϭ n⌽ , ⌽ ϭ , [1] 2 2 0 0 e which comes from the coupling with the spin degrees of freedom. These discrete symmetries lead to the larger spectrum of the where e is the charge of the electron. strings and nexuses in superconductors, as compared with the In 1974, it was shown by ‘t Hooft (2) and Polyakov (3) that a Standard Model. magnetic monopole with quantization of the magnetic charge, according to Eq. 1, can really occur as a physical object if the Fractional Vortices in Chiral Superfluids͞Superconductors. Order pa- U(1) group of electromagnetism is a part of the higher symmetry rameter in chiral superfluids͞superconductors. The order param- group. The magnetic flux of a monopole in terms of the eter describing the vacuum manifold in a chiral p-wave super- elementary magnetic flux coincides with the topological charge fluid (3He-A) is the so-called gap function, which, in the of the monopole: this quantity remains constant under any representation S ϭ 1(S is the spin momentum of Cooper pairs) smooth deformation of the quantum fields. Such monopoles can and L ϭ 1(L is the orbital angular momentum of Cooper pairs), appear only in Grand Unified Theories, where all interactions depends linearly on spin ␴ and momentum k, namely: are united by, say, the SU(5) group. In the Standard Model of electroweak interactions, such mono- ͑1͒ ͑2͒ ⌬͑k r͒ ϭ ␣ ͑r͒␴␣ ␣ ϭ ⌬ˆ␣͑ˆ ϩ ˆ ͒ [2] poles do not exist, but the combined objects monopole ϩ string can , A i ki, A i d ei iei . ,be constructed without violating of the condition ٌ⅐B ϭ 0. Further following the terminology of ref. 4, I shall call such a combined *To whom reprint requests should be addressed. E-mail: [email protected].fi. PHYSICS object a nexus. In a nexus, the magnetic monopole looks like a Dirac The publication costs of this article were defrayed in part by page charge payment. This monopole, but the Dirac string is physical and is represented by the article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. cosmic string. An example is the electroweak monopole discussed §1734 solely to indicate this fact. PNAS ͉ March 14, 2000 ͉ vol. 97 ͉ no. 6 ͉ 2431–2436 Downloaded by guest on September 24, 2021 ␪ ⌬͑k, r͒ ϭ ͓sin2 k⅐a͑r͒ Ϫ sin2 k⅐b͑r͔͒ei . [4] Because of the breaking of time reversal symmetry in chiral crystalline superconductors, persistent electric current arises not only because of the phase coherence but also because of deformations of the crystal: e ប [j ϭ ␳ ͩv Ϫ Aͪ ϩ Ka ٌb , v ϭ ٌ␪. [5 s s mc i i s 2m The parameter K ϭ 0 in nonchiral d-wave superconductors. ϫ ϫ 3 The symmetry breaking scheme SO(3)S SO(3)L U(1)N ϫ Ϫ ϫ U(1)S3 U(1)N L3 Z2, realized by the order parameter in Eq. 2, results in linear topological defects (vortices or strings) of group Z4 (8). Vortices are classified by the circulation quantum ϭ ͞ ͛ ⅐ number N (2m h) dr vs around the vortex core. The simplest realization of the vortex with integer N is eˆ(1) ϩ ieˆ(2) ϭ (xˆ ϩ iyˆ)eiN␾, where ␾ is the azimuthal angle around the string. Vortices with even N are topologically unstable and can be continuously transformed to a nonsingular configuration. N ϭ 1͞2 and N ϭ 1͞4 vortices. Vortices with a half-integer N result from the above identification of the points. They are combinations of the ␲-vortex and ␲-disclination in the dˆ field: ␾ ␾ ͑ ͒ ͑ ͒ ␾ dˆ ϭ ˆx cos ϩ ˆy sin , ˆe 1 ϩ ieˆ 2 ϭ ei /2͑ˆx ϩ iyˆ͒. [6] 2 2 The N ϭ 1͞2 vortex is the counterpart of Alice strings considered in particle physics (9): a particle that moves around an Alice string flips its charge. In 3He-A, the quasiparticle going ͞ around a 1 2 vortex flips its S3 charge, that is, its spin. The d-vector, which plays the role of the quantization axis for the spin of a quasiparticle, rotates by ␲ around the vortex, such that a quasiparticle adiabatically moving around the vortex insensibly finds its spin reversed with respect to the fixed environment. As Fig. 1. Dirac monopole, ‘t Hooft–Polyakov monopole, and electroweak a consequence, several phenomena (e.g., global Aharonov– monopole with physical Dirac string. Bohm effect) discussed in the particle physics literature have corresponding discussions in condensed matter literature (see refs. 10 and 11 for 3He-A and refs. 12 and 13 in particle physics). ˆ (1) Here, d is the unit vector of the spin-space anisotropy and eˆ In type II superconductors, vortices with N circulation quanta and eˆ(2) are mutually orthogonal unit vectors in the orbital space; ⌽ ϭ ͞ ⌽ ͞ carry a magnetic flux N (N 2) 0; the extra factor 1 2 comes they determine the superfluid velocity of the chiral condensate from the Cooper pairing nature of superconductors. According (ϭប (1)ٌ (2 vs /2 meˆi eˆi , where 2m is the mass of the Cooper pair and to the London equations, screening of the electric current far ˆ ϭ (1) ϫ (2) ϭ ͞ the orbital momentum vector is l eˆ eˆ .
Load more

Recommended publications
  • Mesons Modeled Using Only Electrons and Positrons with Relativistic Onium Theory Ray Fleming [email protected]
    All mesons modeled using only electrons and positrons with relativistic onium theory Ray Fleming [email protected] All mesons were investigated to determine if they can be modeled with the onium model discovered by Milne, Feynman, and Sternglass with only electrons and positrons. They discovered the relativistic positronium solution has the mass of a neutral pion and the relativistic onium mass increases in steps of me/α and me/2α per particle which is consistent with known mass quantization. Any pair of particles or resonances can orbit relativistically and particles and resonances can collocate to form increasingly complex resonances. Pions are positronium, kaons are pionium, D mesons are kaonium, and B mesons are Donium in the onium model. Baryons, which are addressed in another paper, have a non-relativistic nucleon combined with mesons. The results of this meson analysis shows that the compo- sition, charge, and mass of all mesons can be accurately modeled. Of the 220 mesons mod- eled, 170 mass estimates are within 5 MeV/c2 and masses of 111 of 121 D, B, charmonium, and bottomonium mesons are estimated to within 0.2% relative error. Since all mesons can be modeled using only electrons and positrons, quarks and quark theory are unnecessary. 1. Introduction 2. Method This paper is a report on an investigation to find Sternglass and Browne realized that a neutral pion whether mesons can be modeled as combinations of (π0), as a relativistic electron-positron pair, can orbit a only electrons and positrons using onium theory. A non-relativistic particle or resonance in what Browne companion paper on baryons is also available.
    [Show full text]
  • Quasiparticle Anisotropic Hydrodynamics in Ultra-Relativistic
    QUASIPARTICLE ANISOTROPIC HYDRODYNAMICS IN ULTRA-RELATIVISTIC HEAVY-ION COLLISIONS A dissertation submitted to Kent State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy by Mubarak Alqahtani December, 2017 c Copyright All rights reserved Except for previously published materials Dissertation written by Mubarak Alqahtani BE, University of Dammam, SA, 2006 MA, Kent State University, 2014 PhD, Kent State University, 2014-2017 Approved by , Chair, Doctoral Dissertation Committee Dr. Michael Strickland , Members, Doctoral Dissertation Committee Dr. Declan Keane Dr. Spyridon Margetis Dr. Robert Twieg Dr. John West Accepted by , Chair, Department of Physics Dr. James T. Gleeson , Dean, College of Arts and Sciences Dr. James L. Blank Table of Contents List of Figures . vii List of Tables . xv List of Publications . xvi Acknowledgments . xvii 1 Introduction ......................................1 1.1 Units and notation . .1 1.2 The standard model . .3 1.3 Quantum Electrodynamics (QED) . .5 1.4 Quantum chromodynamics (QCD) . .6 1.5 The coupling constant in QED and QCD . .7 1.6 Phase diagram of QCD . .9 1.6.1 Quark gluon plasma (QGP) . 12 1.6.2 The heavy-ion collision program . 12 1.6.3 Heavy-ion collisions stages . 13 1.7 Some definitions . 16 1.7.1 Rapidity . 16 1.7.2 Pseudorapidity . 16 1.7.3 Collisions centrality . 17 1.7.4 The Glauber model . 19 1.8 Collective flow . 21 iii 1.8.1 Radial flow . 22 1.8.2 Anisotropic flow . 22 1.9 Fluid dynamics . 26 1.10 Non-relativistic fluid dynamics . 26 1.10.1 Relativistic fluid dynamics .
    [Show full text]
  • Energy-Dependent Kinetic Model of Photon Absorption by Superconducting Tunnel Junctions
    Energy-dependent kinetic model of photon absorption by superconducting tunnel junctions G. Brammertz Science Payload and Advanced Concepts Office, ESA/ESTEC, Postbus 299, 2200AG Noordwijk, The Netherlands. A. G. Kozorezov, J. K. Wigmore Department of Physics, Lancaster University, Lancaster, United Kingdom. R. den Hartog, P. Verhoeve, D. Martin, A. Peacock Science Payload and Advanced Concepts Office, ESA/ESTEC, Postbus 299, 2200AG Noordwijk, The Netherlands. A. A. Golubov, H. Rogalla Department of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands. Received: 02 June 2003 – Accepted: 31 July 2003 Abstract – We describe a model for photon absorption by superconducting tunnel junctions in which the full energy dependence of all the quasiparticle dynamic processes is included. The model supersedes the well-known Rothwarf-Taylor approach, which becomes inadequate for a description of the small gap structures that are currently being developed for improved detector resolution and responsivity. In these junctions relaxation of excited quasiparticles is intrinsically slow so that the energy distribution remains very broad throughout the whole detection process. By solving the energy- dependent kinetic equations describing the distributions, we are able to model the temporal and spectral evolution of the distribution of quasiparticles initially generated in the photo-absorption process. Good agreement is obtained between the theory and experiment. PACS numbers: 85.25.Oj, 74.50.+r, 74.40.+k, 74.25.Jb To be published in the November issue of Journal of Applied Physics 1 I. Introduction The development of superconducting tunnel junctions (STJs) for application as photon detectors for astronomy and materials analysis continues to show great promise1,2.
    [Show full text]
  • Vortices and Quasiparticles in Superconducting Microwave Resonators
    Syracuse University SURFACE Dissertations - ALL SURFACE May 2016 Vortices and Quasiparticles in Superconducting Microwave Resonators Ibrahim Nsanzineza Syracuse University Follow this and additional works at: https://surface.syr.edu/etd Part of the Physical Sciences and Mathematics Commons Recommended Citation Nsanzineza, Ibrahim, "Vortices and Quasiparticles in Superconducting Microwave Resonators" (2016). Dissertations - ALL. 446. https://surface.syr.edu/etd/446 This Dissertation is brought to you for free and open access by the SURFACE at SURFACE. It has been accepted for inclusion in Dissertations - ALL by an authorized administrator of SURFACE. For more information, please contact [email protected]. Abstract Superconducting resonators with high quality factors are of great interest in many areas. However, the quality factor of the resonator can be weakened by many dissipation chan- nels including trapped magnetic flux vortices and nonequilibrium quasiparticles which can significantly impact the performance of superconducting microwave resonant circuits and qubits at millikelvin temperatures. Quasiparticles result in excess loss, reducing resonator quality factors and qubit lifetimes. Vortices trapped near regions of large mi- crowave currents also contribute excess loss. However, vortices located in current-free areas in the resonator or in the ground plane of a device can actually trap quasiparticles and lead to a reduction in the quasiparticle loss. In this thesis, we will describe exper- iments involving the controlled trapping of vortices for reducing quasiparticle density in the superconducting resonators. We provide a model for the simulation of reduc- tion of nonequilibrium quasiparticles by vortices. In our experiments, quasiparticles are generated either by stray pair-breaking radiation or by direct injection using normal- insulator-superconductor (NIS)-tunnel junctions.
    [Show full text]
  • B2.IV Nuclear and Particle Physics
    B2.IV Nuclear and Particle Physics A.J. Barr February 13, 2014 ii Contents 1 Introduction 1 2 Nuclear 3 2.1 Structure of matter and energy scales . 3 2.2 Binding Energy . 4 2.2.1 Semi-empirical mass formula . 4 2.3 Decays and reactions . 8 2.3.1 Alpha Decays . 10 2.3.2 Beta decays . 13 2.4 Nuclear Scattering . 18 2.4.1 Cross sections . 18 2.4.2 Resonances and the Breit-Wigner formula . 19 2.4.3 Nuclear scattering and form factors . 22 2.5 Key points . 24 Appendices 25 2.A Natural units . 25 2.B Tools . 26 2.B.1 Decays and the Fermi Golden Rule . 26 2.B.2 Density of states . 26 2.B.3 Fermi G.R. example . 27 2.B.4 Lifetimes and decays . 27 2.B.5 The flux factor . 28 2.B.6 Luminosity . 28 2.C Shell Model § ............................. 29 2.D Gamma decays § ............................ 29 3 Hadrons 33 3.1 Introduction . 33 3.1.1 Pions . 33 3.1.2 Baryon number conservation . 34 3.1.3 Delta baryons . 35 3.2 Linear Accelerators . 36 iii CONTENTS CONTENTS 3.3 Symmetries . 36 3.3.1 Baryons . 37 3.3.2 Mesons . 37 3.3.3 Quark flow diagrams . 38 3.3.4 Strangeness . 39 3.3.5 Pseudoscalar octet . 40 3.3.6 Baryon octet . 40 3.4 Colour . 41 3.5 Heavier quarks . 43 3.6 Charmonium . 45 3.7 Hadron decays . 47 Appendices 48 3.A Isospin § ................................ 49 3.B Discovery of the Omega § ......................
    [Show full text]
  • Ions, Protons, and Photons As Signatures of Monopoles
    universe Article Ions, Protons, and Photons as Signatures of Monopoles Vicente Vento Departamento de Física Teórica-IFIC, Universidad de Valencia-CSIC, 46100 Burjassot (Valencia), Spain; [email protected] Received: 8 October 2018; Accepted: 1 November 2018; Published: 7 November 2018 Abstract: Magnetic monopoles have been a subject of interest since Dirac established the relationship between the existence of monopoles and charge quantization. The Dirac quantization condition bestows the monopole with a huge magnetic charge. The aim of this study was to determine whether this huge magnetic charge allows monopoles to be detected by the scattering of charged ions and protons on matter where they might be bound. We also analyze if this charge favors monopolium (monopole–antimonopole) annihilation into many photons over two photon decays. 1. Introduction The theoretical justification for the existence of classical magnetic poles, hereafter called monopoles, is that they add symmetry to Maxwell’s equations and explain charge quantization. Dirac showed that the mere existence of a monopole in the universe could offer an explanation of the discrete nature of the electric charge. His analysis leads to the Dirac Quantization Condition (DQC) [1,2] eg = N/2, N = 1, 2, ..., (1) where e is the electron charge, g the monopole magnetic charge, and we use natural units h¯ = c = 1 = 4p#0. Monopoles have been a subject of experimental interest since Dirac first proposed them in 1931. In Dirac’s formulation, monopoles are assumed to exist as point-like particles and quantum mechanical consistency conditions lead to establish the value of their magnetic charge. Because of of the large magnetic charge as a consequence of Equation (1), monopoles can bind in matter [3].
    [Show full text]
  • Coupling Experiment and Simulation to Model Non-Equilibrium Quasiparticle Dynamics in Superconductors
    Coupling Experiment and Simulation to Model Non-Equilibrium Quasiparticle Dynamics in Superconductors A. Agrawal9, D. Bowring∗1, R. Bunker2, L. Cardani3, G. Carosi4, C.L. Chang15, M. Cecchin1, A. Chou1, G. D’Imperio3, A. Dixit9, J.L DuBois4, L. Faoro16,7, S. Golwala6, J. Hall13,14, S. Hertel12, Y. Hochberg11, L. Ioffe5, R. Khatiwada1, E. Kramer11, N. Kurinsky1, B. Lehmann10, B. Loer2, V. Lordi4, R. McDermott7, J.L. Orrell2, M. Pyle17, K. G. Ray4, Y. J. Rosen4, A. Sonnenschein1, A. Suzuki8, C. Tomei3, C. Wilen7, and N. Woollett4 1Fermi National Accelerator Laboratory 2Pacific Northwest National Laboratory 3Sapienza University of Rome 4Lawrence Livermore National Laboratory 5Google, Inc. 6California Institute of Technology 7University of Wisconsin, Madison 8Lawrence Berkeley National Laboratory 9University of Chicago 10University of California, Santa Cruz 11Hebrew University of Jerusalem 12University of Massachusetts, Amherst 13SNOLAB 14Laurentian University 15Argonne National Laboratory 16Laboratoire de Physique Therique et Hautes Energies, Sorbornne Universite 17University of California, Berkeley August 31, 2020 Thematic Areas: (check all that apply /) (CF1) Dark Matter: Particle Like (CF2) Dark Matter: Wavelike (IF1) Quantum Sensors (IF2) Photon Detectors (IF9) Cross Cutting and Systems Integration (UF02) Underground Facilities for Cosmic Frontier (UF05) Synergistic Research ∗Corresponding author: [email protected] 1 Abstract In superconducting devices, broken Cooper pairs (quasiparticles) may be considered signal (e.g., transition edge sensors, kinetic inductance detectors) or noise (e.g., quantum sensors, qubits). In order to improve design for these devices, a better understanding of quasiparticle production and transport is required. We propose a multi-disciplinary collaboration to perform measurements in low-background facilities that will be used to improve modeling and simulation tools, suggest new measurements, and drive the design of future improved devices.
    [Show full text]
  • "Normal-Metal Quasiparticle Traps for Superconducting Qubits"
    Normal-Metal Quasiparticle Traps For Superconducting Qubits: Modeling, Optimization, and Proximity Effect Von der Fakultät für Mathematik, Informatik und Naturwissenschaften der RWTH Aachen University zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften genehmigte Dissertation vorgelegt von Amin Hosseinkhani, M.Sc. Berichter: Universitätsprofessor Dr. David DiVincenzo, Universitätsprofessorin Dr. Kristel Michielsen Tag der mündlichen Prüfung: March 01, 2018 Diese Dissertation ist auf den Internetseiten der Universitätsbibliothek online verfügbar. Metallische Quasiteilchenfallen für supraleitende Qubits: Modellierung, Optimisierung, und Proximity-Effekt Kurzfassung: Bogoliubov Quasiteilchen stören viele Abläufe in supraleitenden Elementen. In supraleitenden Qubits wechselwirken diese Quasiteilchen beim Tunneln durch den Josephson- Kontakt mit dem Phasenfreiheitsgrad, was zu einer Relaxation des Qubits führt. Für Tempera- turen im Millikelvinbereich gibt es substantielle Hinweise für die Präsenz von Nichtgleichgewicht- squasiteilchen. Während deren Entstehung noch nicht einstimmig geklärt ist, besteht dennoch die Möglichkeit die von Quasiteilchen induzierte Relaxation einzudämmen indem man die Qu- asiteilchen von den aktiven Bereichen des Qubits fernhält. In dieser Doktorarbeit studieren wir Quasiteilchenfallen, welche durch einen Kontakt eines normalen Metalls (N) mit der supraleit- enden Elektrode (S) eines Qubits definiert sind. Wir entwickeln ein Modell, das den Einfluss der Falle auf die Quasiteilchendynamik beschreibt,
    [Show full text]
  • STRANGE MESON SPECTROSCOPY in Km and K$ at 11 Gev/C and CHERENKOV RING IMAGING at SLD *
    SLAC-409 UC-414 (E/I) STRANGE MESON SPECTROSCOPY IN Km AND K$ AT 11 GeV/c AND CHERENKOV RING IMAGING AT SLD * Youngjoon Kwon Stanford Linear Accelerator Center Stanford University Stanford, CA 94309 January 1993 Prepared for the Department of Energy uncer contract number DE-AC03-76SF005 15 Printed in the United States of America. Available from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, Virginia 22161. * Ph.D. thesis ii Abstract This thesis consists of two independent parts; development of Cherenkov Ring Imaging Detector (GRID) system and analysis of high-statistics data of strange meson reactions from the LASS spectrometer. Part I: The CIUD system is devoted to charged particle identification in the SLAC Large Detector (SLD) to study e+e- collisions at ,/Z = mzo. By measuring the angles of emission of the Cherenkov photons inside liquid and gaseous radiators, r/K/p separation will be achieved up to N 30 GeV/c. The signals from CRID are read in three coordinates, one of which is measured by charge-division technique. To obtain a N 1% spatial resolution in the charge- division, low-noise CRID preamplifier prototypes were developed and tested re- sulting in < 1000 electrons noise for an average photoelectron signal with 2 x lo5 gain. To help ensure the long-term stability of CRID operation at high efficiency, a comprehensive monitoring and control system was developed. This system contin- uously monitors and/or controls various operating quantities such as temperatures, pressures, and flows, mixing and purity of the various fluids.
    [Show full text]
  • Lecture 2 - Energy and Momentum
    Lecture 2 - Energy and Momentum E. Daw February 16, 2012 1 Energy In discussing energy in a relativistic course, we start by consid- ering the behaviour of energy in the three regimes we worked with last time. In the first regime, the particle velocity v is much less than c, or more precisely β < 0:3. In this regime, the rest energy ER that the particle has by virtue of its non{zero rest mass is much greater than the kinetic energy T which it has by virtue of its kinetic energy. The rest energy is given by Einstein's famous equation, 2 ER = m0c (1) So, here is an example. An electron has a rest mass of 0:511 MeV=c2. What is it's rest energy?. The important thing here is to realise that there is no need to insert a factor of (3×108)2 to convert from rest mass in MeV=c2 to rest energy in MeV. The units are such that 0.511 is already an energy in MeV, and to get to a mass you would need to divide by c2, so the rest mass is (0:511 MeV)=c2, and all that is left to do is remove the brackets. If you divide by 9 × 1016 the answer is indeed a mass, but the units are eV m−2s2, and I'm sure you will appreciate why these units are horrible. Enough said about that. Now, what about kinetic energy? In the non{relativistic regime β < 0:3, the kinetic energy is significantly smaller than the rest 1 energy.
    [Show full text]
  • Quasi-Dirac Monopoles
    research highlights Defective yet strong fundamental particle, the magnetic polymeric film, the researchers embedded Nature Commun. 5, 3186 (2014) monopole, with non-zero magnetic silver nanoparticles that have a localized monopole charge, has grasped the attention surface plasmon resonance in the blue With a tensile strength of over 100 GPa, of many. The existence of magnetic spectral range; the fabricated film therefore a pristine graphene layer is the strongest monopoles is now not only supported by the scatters this colour while being almost material known. However, most graphene work of Dirac, but by both the grand unified completely transparent in the remaining fabrication processes inevitably produce theory and string theory. However, both visible spectral range. The researchers a defective layer. Also, structural defects theories realize that magnetic monopoles suggest that dispersion in a single matrix of are desirable in some of the material’s might be too few and too massive to be metallic nanoparticles with sharp plasmonic technological applications, as defects allow detected or created in a lab, so physicists resonances tuned at different wavelengths for the opening of a bandgap or act as pores started to explore approaches to obtain will lead to the realization of multicoloured for molecular sieving, for example. Now, by such particles using condensed-matter transparent displays. LM tuning the exposure of graphene to oxygen systems. Now, Ray and co-workers report plasma to control the creation of defects, the latest observation of a Dirac monopole Ardavan Zandiatashbar et al. show that a quasiparticle (pictured), this time in a Facet formation Adv. Mater. http://doi.org/rb5 (2014) single layer of graphene bearing sp3-type spinor Bose–Einstein condensate.
    [Show full text]
  • Relativistic Particle Orbits
    H. Kleinert, PATH INTEGRALS August 12, 2014 (/home/kleinert/kleinert/books/pathis/pthic19.tex) Agri non omnes frugiferi sunt Not all fields are fruitful Cicero (106 BC–43 BC), Tusc. Quaest., 2, 5, 13 19 Relativistic Particle Orbits Particles moving at large velocities near the speed of light are called relativistic particles. If such particles interact with each other or with an external potential, they exhibit quantum effects which cannot be described by fluctuations of a single particle orbit. Within short time intervals, additional particles or pairs of particles and antiparticles are created or annihilated, and the total number of particle orbits is no longer invariant. Ordinary quantum mechanics which always assumes a fixed number of particles cannot describe such processes. The associated path integral has the same problem since it is a sum over a given set of particle orbits. Thus, even if relativistic kinematics is properly incorporated, a path integral cannot yield an accurate description of relativistic particles. An extension becomes necessary which includes an arbitrary number of mutually linked and branching fluctuating orbits. Fortunately, there exists a more efficient way of dealing with relativistic particles. It is provided by quantum field theory. We have demonstrated in Section 7.14 that a grand-canonical ensemble of particle orbits can be described by a functional integral of a single fluctuating field. Branch points of newly created particle lines are accounted for by anharmonic terms in the field action. The calculation of their effects proceeds by perturbation theory which is systematically performed in terms of Feynman diagrams with calculation rules very similar to those in Section 3.18.
    [Show full text]