DOCSLIB.ORG

Vortex Nucleation in a Superfluid

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Vortex Nucleation in a Superfluid Vortex Nucleation in a Superfluid by Dominic Marchand B.Sc. in Computer Engineering, Universite Laval, 2002 B.Sc. in Physics, The University of British Columbia, 2004 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in The Faculty of Graduate Studies (Physics) The University Of British Columbia October 2006 © Dominic Marchand, 2006 Abstract Superfluids have very peculiar rotational properties as the Hess-Fairbank experiment spectac• ularly demonstrates. In this experiment, a rotating vessel filled with helium is cooled down past the critical temperature. Remarkably, as the liquid becomes superfluid, it gradually stops its rotation. This expulsion of vorticity, analogous to the Meissner effect, provides a funda• mental experimental definition of superfluidity. As a consequence, superfluids not only posses quasiparticles like phonons, but also quantized vortex excitations. This thesis examines the creation mechanism of vortices, or nucleation, in the low temper• ature limit. At these temperatures, thermal activation of vortices is ruled out and nucleation must be a tunneling effect. Unfortunately, there is no theory to describe this nucleation process. Vortex nucleation is believed to more likely occur in the vicinity of irregularities of the vessel. We therefore consider a few simple, yet experimentally realistic, two-dimensional configurations to calculate nucleation rates. Close to zero temperature and within a certain approximation, the superfluid is inviscid and incompressible such that it can naturally be treated as an ideal two-dimensional fluid flow. Calculating the energy of static vortex configurations can then be done with standard hydrodynamics. The kinetic energy of the flow as a function of the position of the vortex then describes a potential barrier for vortex nucleation. Under rotation, the vortex-free state becomes metastable and can decay to a state with one or more vortices. In this thesis, we carry out a semiclassical calculation of the nucleation rate exponent. We use the WKB method along the path of least action created by the presence of a bump or wedge. This work is but a first approximation as fluctuations around this path can be added as well. The main purpose has been to lay down the groundwork required to include the dissipative effect of the coupling to phonons, which is paramount to an accurate description of the phenomenon. This effect could then be included using the Caldeira-Leggett dissipative tunneling effect [4]. ii Table of Contents Abstract ii Table of Contents iii List of Figures vi Acknowledgements viii 1 Introduction 1 1.1 A Brief History of Superfluidity 1 1.1.1 The Birth of the Field of Quantum Fluids 1 1.1.2 Toward a Macroscopic Theory, the Two-Fluid Model 2 1.1.3 The Landau-Tisza Controversy (1941-1947) 3 1.1.4 Towards a Microscopic Justification 4 1.1.5 Another Superfluid 5 1.2 Theory of Superfluidity 5 1.2.1 Definition of Superfluidity 5 1.2.2 The Two-Fluid Model 6 1.2.3 Quantum Fluid 8 1.2.4 Similarities with the Ideal Bose-Einstein Gas 8 1.2.5 Wave Function 10 1.2.6 Excitations and Quasiparticles 12 1.2.7 The Quantization of Circulation and the Vortex State 13 1.3 Investigations of Vortices and Vortex Nucleation in Superfluid 4He 14 1.3.1 Rotational Motion and Quantization 15 1.3.2 Observation of Vortices 15 1.3.3 Vortex Nucleation and the Limitation of Superflow 15 1.3.4 Nucleation of Quantized Vortex Rings 17 1.3.5 Quantum Tunnelling 19 1.4 Theoretical Studies of Vortex Nucleation 20 1.5 Our Motivation 21 2 Hydrodynamics and Superflow Configurations 22 2.1 Two-Dimensional Ideal Fluid Flow Description 22 2.1.1 Convention for Flux and Density in Two Dimensions 23 iii 2.1.2 Description of a Two-Dimensional Ideal Fluid Flow 23 2.1.3 The Velocity Potential $ 24 2.1.4 The Stream Function * 25 2.1.5 Boundary Conditions 25 2.1.6 Conformal Mapping 26 2.1.7 Multiply-Connected Regions 27 2.2 Description of Quantized Vortices 29 2.2.1 Properties of a Rectilinear Vortex 29 2.2.2 Velocity Potential and Stream Function 30 2.2.3 Example: Off-Center Vortex in a Cylinder 31 2.3 Kinetic Energy 35 2.3.1 Energy of an Off-Center Vortex in a Cylinder 35 2.3.2 Line Integral on the Boundary 40 2.3.3 Branch Cuts 41 3 Simple Yet Useful Configurations 43 3.1 Vortex in a Cylinder With a Wedge 43 3.1.1 Starting Configuration With No Wedge 44 3.1.2 Conformal Mapping 44 3.1.3 Corrections to the Position of the Vortex 50 3.1.4 Kinetic Energy 51 3.1.5 Rotation of the Cylinder 55 3.2 Circular Bump on a Flat Wall 56 3.2.1 Complex Velocity Potential 57 3.2.2 Kinetic Energy 60 4 Vortex Nucleation and Tunneling 66 4.1 The WKB Approximation 66 4.1.1 Exponent 66 4.1.2 WKB in Higher Dimensions 67 4.1.3 Vortex Nucleation 67 4.2 Tunneling Rate For a Perfect Cylinder 67 4.2.1 Properties of the Barrier 67 4.2.2 Approximations to the Potential 69 4.2.3 Numerical Integration 72 4.2.4 Curve Fits and Approximations 72 4.3 Tunneling Rate For a Circular Bump on a Flat Wall 74 4.3.1 Properties of the Barrier 74 4.3.2 Numerical Integration 75 4.3.3 Curve Fits and Approximations 76 4.4 Effective Mass of a Vortex 85 4.4.1 Inertial Mass of a Vortex for a Non-Uniform Condensate 86 4.5 Future Work and Conclusions 88 iv Bibliography 90 v List of Figures 1.1 Phase diagram and specific heat of 4He 2 1.2 Two-fluid model 7 1.3 Energy spectrum of quasiparticles in superfluid helium 12 1.4 Schematic of a superfluid gyroscope 17 1.5 Possible metastates for the superfluid gyroscope 18 1.6 Alternative models of vortex ring nucleation by ion 18 2.1 Simply-connected and multiply-connected regions 27 2.2 Method of images for a vortex inside a cylinder 32 2.3 Geometry for an off-center vortex with an image vortex 33 2.4 Equipotential lines and lines of force for a cylindrical capacitor 38 2.5 Equipotential and stream lines for an off-center vortex 39 2.6 Branch cut for a vortex in a cylinder 42 3.1 Mapping to a cylinder with a wedge 43 3.2 Mapping from a circle to a circle with a wedge 45 3.3 Mapping from a circle to the upper half-plane 46 3.4 Mapping to the upper half-plane with a wedge 46 3.5 Mapping to a circle with a wedge 49 3.6 Coordinates offset due to the mapping 50 3.7 Energy of a vortex in a cylinder with a wedge 53 3.8 Energy of a vortex on the x axis in a cylinder with a wedge 54 3.9 Modification to the energy of a vortex in a rotating cylinder 56 3.10 Stream functions of a flow past a cylinder and a moving cylinder 58 3.11 Vortices configuration for a cylindrical bump on a flat wall 59 3.12 Stream function of a vortex near a moving cylinder 60 3.13 Branch cut for the vortex configuration near a cylinder 60 3.14 Energy of a vortex near a semi-circular bump 64 3.15 Lines of constant energy for a vortex near a semi-circular bump 65 4.1 Potential for a vortex in a perfect cylinder as a function of u 68 4.2 Approximations of V(x) for a vortex in a perfect cylinder 70 4.3 j(u) for a perfect cylinder where the potential is defined in 2 parts: linear and quadratic 71 vi 4.4 j(u) for a perfect cylinder where the potential is defined in 2 parts: quadratic and quadratic 72 4.5 Curve fits of 7(7/) for a perfect cylinder using 7 = A|iz|~A +70 73 4.6 Fit parameters for a perfect cylinder with 7 = A|'u|_A + 70 77 4.7 Fit parameters for a perfect cylinder using 7 = A|ii|~2 + 70 and curve fit of these parameters 78 4.8 Curve fits of 7(14) for a perfect cylinder using 7 = A|u|~2 + 70 and using the results of a fit for A and 70 79 4.9 Curve fits of j(u) for a circular bump using 7 = A|u|_A + 70 80 4.10 Fit parameters for a circular bump using 7 = A|u|~A + 70 and curve fit of these parameters 81 4.11 Curve fits of j(u) for a circular bump using 7 = A|u|-A+70 and using the results of a fit for A, 70 and A 82 4.12 Fit parameters for a circular bump using 7 = + 70 and curve fit of these parameters 83 4.13 Curve fits of 7(14) for a circular bump using 7 = -f 70 and using the results of a fit for A and 70 84 vii Acknowledgements I would like to express my thanks to my supervisor, Philip Stamp, for his invaluable help and advice, and to Mona Berciu, for agreeing to be my second reader. Thanks to my friend and colleague Rodrigo Pereira with whom I had fruitful discussions on my research topic. In the proofreading of this thesis, I have had the help and advice of many friends and colleagues.
Load more

Recommended publications
  • Renormalizability of the Center-Vortex Free Sector of Yang-Mills Theory
    PHYSICAL REVIEW D 101, 085007 (2020) Renormalizability of the center-vortex free sector of Yang-Mills theory † ‡ D. Fiorentini ,* D. R. Junior, L. E. Oxman , and R. F. Sobreiro § UFF—Universidade Federal Fluminense, Instituto de Física, Campus da Praia Vermelha, Avenida Litorânea s/n, 24210-346 Niterói, RJ, Brasil. (Received 11 February 2020; accepted 30 March 2020; published 17 April 2020) In this work, we analyze a recent proposal to detect SUðNÞ continuum Yang-Mills sectors labeled by center vortices, inspired by Laplacian-type center gauges in the lattice. Initially, after the introduction of appropriate external sources, we obtain a rich set of sector-dependent Ward identities, which can be used to control the form of the divergences. Next, we show the all-order multiplicative renormalizability of the center-vortex free sector. These are important steps towards the establishment of a first-principles, well-defined, and calculable Yang-Mills ensemble. DOI: 10.1103/PhysRevD.101.085007 I. INTRODUCTION was obtained in Euclidean spacetime [12,13], which provides a calculational tool similar to the one used in As is well known, the Fadeev-Popov procedure to the perturbative regime. Beyond the linear covariant quantize Yang-Mills (YM) theories [1], so successful in gauges, many efforts were also devoted to the maximal making contact with experiments at high energies, cannot Abelian gauges; see Ref. [14] and references therein. BRST be extended to the infrared regime [2,3]. In covariant invariance is an important feature to have predictive power gauges, this was established by Singer’s theorem [4]: for (renormalizability), as well as to show the independence of any gauge fixing, there are orbits with more than one gauge observables on gauge-fixing parameters.
    [Show full text]
  • Download This Article in PDF Format
    EPJ Web of Conferences 245, 06009 (2020) https://doi.org/10.1051/epjconf/202024506009 CHEP 2019 Emergent Structure in QCD James Biddle1;∗, Waseem Kamleh1;∗∗, and Derek Leinweber1;∗∗∗ 1Centre for the Subatomic Structure of Matter, Department of Physics, The University of Adelaide, SA 5005, Australia Abstract. The structure of the SU(3) gauge-field vacuum is explored through visualisations of centre vortices and topological charge density. Stereoscopic visualisations highlight interesting features of the vortex vacuum, especially the frequency with which singular points appear and the important connection between branching points and topological charge. This work demonstrates how visualisations of the QCD ground-state fields can reveal new perspectives of centre-vortex structure. 1 Introduction Quantum Chromodynamics (QCD) is the fundamental relativistic quantum field theory un- derpinning the strong interactions of nature. The gluons of QCD carry colour charge and self-couple. This self-coupling makes the empty vacuum unstable to the formation of non- trivial quark and gluon condensates. These non-trivial ground-state “QCD-vacuum” field configurations form the foundation of matter. There are eight chromo-electric and eight chromo-magnetic fields composing the QCD vacuum. An stereoscopic illustration of one of these chromo-magnetic fields is provided in Fig. 1. Animations of the fields are also available [1–3]. The essential, fundamentally-important, nonperturbative features of the QCD vacuum fields are the dynamical generation of mass through chiral symmetry breaking, and the con- finement of quarks. But what is the fundamental mechanism of QCD that underpins these phenomena? What aspect of the QCD vacuum causes quarks to be confined? Which aspect is responsible for dynamical mass generation? Do the underlying mechanisms share a common origin? One of the most promising candidates is the centre vortex perspective [4, 5].
    [Show full text]
  • Center Vortex Detection in Smooth Lattice Configurations
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 25 March 2021 doi:10.20944/preprints202103.0615.v1 Article A POSSIBLE RESOLUTION TO TROUBLES OF SU(2) CENTER VORTEX DETECTION IN SMOOTH LATTICE CONFIGURATIONS Rudolf Golubich ∗ , Manfried Faber Atominstitut, Technische Universität Wien; 1040 Wien; Austria * [email protected] 1 Abstract: The center vortex model of quantum-chromodynamics can explain confinement and chiral 2 symmetry breaking. We present a possible resolution for problems of the vortex detection in 3 smooth configurations and discuss improvements for the detection of center vortices. 4 Keywords: quantum chromodynamics; confinement; center vortex model; vacuum structure; 5 cooling 6 PACS: 11.15.Ha, 12.38.Gc 7 1. Introduction 8 The center vortex model of Quantum Chromodynamics [1,2] explains confinement [3] 9 and chiral symmetry breaking [4–6] by the assumption that the relevant excitations 10 of the QCD vacuum are Center vortices: Closed color magnetic flux lines evolving in 11 time. In four dimensional space-time these closed flux lines form closed surfaces in 12 dual space, see Figure1. In the low temperature phase they percolate space-time in all dimensions. Within lattice simulations the center vortices are detected in maximal center Citation: Golubich, R.; Faber, M. Title. Universe 2021, 1, 0. https://doi.org/ Received: Accepted: Published: Publisher’s Note: MDPI stays neu- tral with regard to jurisdictional claims in published maps and insti- Figure 1. left) After transformation to maximal center gauge and projection to the center degrees of tutional affiliations. freedom, a flux line can be traced by following non-trivial plaquettes.
    [Show full text]
  • Baryonic Hybrids: Gluons As Beads on Strings Between Quarks
    UCLA UCLA Previously Published Works Title Baryonic hybrids: Gluons as beads on strings between quarks Permalink https://escholarship.org/uc/item/1r43x573 Journal Physical Review D, 71(5) ISSN 0556-2821 Author Cornwall, J M Publication Date 2005-03-01 Peer reviewed eScholarship.org Powered by the California Digital Library University of California PHYSICAL REVIEW D 71, 056002 (2005) Baryonic hybrids: Gluons as beads on strings between quarks John M. Cornwall* Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA (Received 20 December 2004; published 8 March 2005) In this paper we analyze the ground state of the heavy-quark qqqG system using standard principles of quark confinement and massive constituent gluons as established in the center-vortex picture. The known string tension KF and approximately-known gluon mass M lead to a precise specification of the long- range nonrelativistic part of the potential binding the gluon to the quarks with no undetermined phenomenological parameters, in the limit of large interquark separation R. Our major tool (also used earlier by Simonov) is the use of proper-time methods to describe gluon propagation within the quark system, along with some elementary group theory describing the gluon Wilson-line as a composite of colocated q and q lines. We show that (aside from color-Coulomb and similar terms) the gluon potential energy in the presence of quarks is accurately described (for small gluon fluctuations) via attaching these three strings to the gluon, which in equilibrium sits at the Steiner point of the Y-shaped string network joining the three quarks.
    [Show full text]
  • Von Smekal, Lorenz Johann
    PUBLISHED VERSION Bowman, Patrick Oswald; Langfeld, Kurt; Leinweber, Derek Bruce; Sternbeck, André; von Smekal, Lorenz Johann Maria; Williams, Anthony Gordon Role of center vortices in chiral symmetry breaking in SU(3) gauge theory Physical Review D, 2011; 84(3):034501 ©2011 American Physical Society http://link.aps.org/doi/10.1103/PhysRevD.84.034501 PERMISSIONS http://publish.aps.org/authors/transfer-of-copyright-agreement http://link.aps.org/doi/10.1103/PhysRevD.62.093023 “The author(s), and in the case of a Work Made For Hire, as defined in the U.S. Copyright Act, 17 U.S.C. §101, the employer named [below], shall have the following rights (the “Author Rights”): [...] 3. The right to use all or part of the Article, including the APS-prepared version without revision or modification, on the author(s)’ web home page or employer’s website and to make copies of all or part of the Article, including the APS-prepared version without revision or modification, for the author(s)’ and/or the employer’s use for educational or research purposes.” th 7 June 2013 http://hdl.handle.net/2440/70896 PHYSICAL REVIEW D 84, 034501 (2011) Role of center vortices in chiral symmetry breaking in SU(3) gauge theory Patrick O. Bowman,1 Kurt Langfeld,2 Derek B. Leinweber,3 Andre´ Sternbeck,3,4 Lorenz von Smekal,3,5 and Anthony G. Williams3 1Centre for Theoretical Chemistry and Physics, and Institute of Natural Sciences, Massey University (Albany), Private Bag 102904, North Shore MSC, New Zealand 2School of Maths & Stats, University of Plymouth, Plymouth, PL4 8AA, England 3Centre for the Subatomic Structure of Matter (CSSM), School of Chemistry & Physics, University of Adelaide 5005, Australia 4Institut fu¨r Theoretische Physik, Universita¨t Regensburg, D-93040 Regensburg, Germany 5Institut fu¨r Kernphysik, Technische Universita¨t Darmstadt, D-64289 Darmstadt, Germany (Received 25 October 2010; published 4 August 2011) We study the behavior of the AsqTad quark propagator in Landau gauge on SU(3) Yang-Mills gauge configurations under the removal of center vortices.
    [Show full text]
  • Non-Abelian Vortices — Five Years Since the Discovery —
    RIKEN. Non-Abelian Vortices — Five Years Since the Discovery — Towards New Developments in Field and String Theories 12/22/2008 @ RIKEN Muneto Nitta (Keio U. @ Hiyoshi) 0 Collaborators TITech Soliton Group Norisuke Sakai(Tokyo Woman Ch.), Keisuke Ohashi(DAMTP), Youichi Isozumi, Toshiaki Fujimori(D3), Takayuki Nagashima(D2) Pisa Group Ken-ichi Konishi, Minoru Eto, Giacomo Marmorini, Walter Vinci, Sven Bjarke Gudnason Other Institutes Kazutoshi Ohta(Tohoku), Naoto Yokoi(Komaba), Masahito Yamazaki(Hongo), Koji Hashimoto(RIKEN), Luca Ferretti(Trieste), Jarah Evslin(Trieste), Takeo Inami(Chuo), Shie Minakami(Chuo), Hadron Physics Eiji Nakano, Taeko Matsuura, Noriko Shiiki Condensed Matter Physics Masahito Ueda, Yuki Kawaguchi, Michikazu Kobayashi (Hongo) Anyone is welcome to join us anytime ! 1 x1. Introduction: What are Vortices? Vortices are topological solitons ² of codimension 2: point-like in d = 2 + 1, string in d = 3 + 1, ² to exist when symmetry is broken G ! H with ¼1(G=H) ' ¼0(H) ' H=H0 6= 0 for simply connected G, ² formed via the Kibble-Zurek mechanism or rotation of media, ² carrying magnetic flux or circulation which is quantized. Defects Textures Gauge Structure ¼n codim n + 1 codim n codim n + 1 ¼0 domain walls(kinks) ¼1 vortices nonlinear kinks(sine-Gordon) ¼2 monopoles lumps(2D skyrmions) ¼3 Skyrmions (textures) YM instantons 1 They appear in various area of physics: 1. condensed matter physics ² superconductor (Abrikosov lattice) Abrikosov(’57) ² superfluid 4He Onsager(’49), Feynman(’55) superfluid 3He ² (skyrmions in) quantum Hall effects ² (Bloch line in) Ferromagnets ² atomic gas Bose-Einstein condensation (cold atom) (’01-) ² quantum turbulence (Kolmogorov law) MIT [Abo-Shaer et.al, Science 292 (2001) 476] 2 2.
    [Show full text]
  • Centre Vortices in Lattice QCD Visualisations and Impact on the Gluon Propagator
    Centre Vortices in Lattice QCD Visualisations and Impact on the Gluon Propagator James Biddle Supervisors: Dr. Waseem Kamleh Prof. Derek B. Leinweber Department of Physics University of Adelaide This dissertation is submitted for the degree of Master of Philosophy March 2019 Table of contents List of figures xiii 1 Introduction1 2 Lattice QCD5 2.1 QCD in the Continuum . .5 2.1.1 Quarks and Gauge Invariance . .5 2.1.2 Field Strength Tensor . .8 2.1.3 Pure Gauge Action . 10 2.2 Lattice Discretisation . 11 2.3 Gauge Fixing . 16 2.3.1 Landau Gauge . 16 3 Topology on the Lattice 19 3.1 Confinement . 20 3.2 Centre Vortices . 21 3.2.1 Motivation for the Model . 21 3.2.2 Locating Centre Vortices . 27 3.2.3 Maximal Centre Gauge . 30 3.2.4 Current Evidence for Centre Vortices . 33 3.3 Further Topological Quantities . 35 3.3.1 Topological Charge . 35 3.3.2 Instantons . 37 3.4 Summary . 38 4 Lattice Configurations and the Gluon Propagator 41 4.1 Lattice Definition of the Gluon Propagator . 41 4.2 Momentum Variables . 43 4.3 Renormalisation . 46 iv Table of contents 4.4 Lattice Parameters and Data Cuts . 47 5 Smoothing 53 5.1 Smoothing Methods . 54 5.1.1 Cooling . 54 5.1.2 Over-Improved Smearing . 57 5.2 Results from the Gluon Propagator . 59 6 Gluon Propagator on Vortex-Modified Backgrounds 63 6.1 Preliminary Results . 63 6.1.1 Partitioning . 66 6.2 Impact of Cooling . 68 6.3 Summary . 73 7 Centre Vortex Visualisations 77 7.1 Spatially-Oriented Vortices .
    [Show full text]
  • Gluon Propagator on a Center-Vortex Background
    PHYSICAL REVIEW D 98, 094504 (2018) Gluon propagator on a center-vortex background James C. Biddle,* Waseem Kamleh, and Derek B. Leinweber Centre for the Subatomic Structure of Matter, Department of Physics, The University of Adelaide, South Australia 5005, Australia (Received 15 June 2018; published 12 November 2018) The impact of SUð3Þ center vortices on the gluon propagator in Landau gauge is investigated on original, vortex-removed and vortex-only lattice gauge field configurations. Vortex identification is found to partition the gluon propagator into short-range strength on the vortex-removed configurations and long- range strength on the vortex-only configurations. The effect of smoothing vortex-only configurations is also studied, and a regime for recovering the form of the smoothed original propagator from vortex-only configurations is introduced. The results reinforce the significance of center vortices in a fundamental understanding of QCD vacuum structure. DOI: 10.1103/PhysRevD.98.094504 I. INTRODUCTION gauge field configurations. The purpose of this investigation is to identify whether it is possible to reproduce a gluon There is now significant evidence supporting the role propagator indicative of confining behavior on vortex-only of center vortices in confinement and dynamical chiral configurations. symmetry breaking in QCD. It is well established that for SUð2Þ gauge theories, center vortices account for both of these properties [1–4] and thus it would seem intuitive that II. LANDAU-GAUGE GLUON PROPAGATOR the same would hold for SU(3) theories as well. Previous The momentum-space gluon propagator on a finite 3 work has successfully shown that vortex removal in SUð Þ lattice with four-dimensional volume V is given by corresponds to a loss of dynamical mass generation and string tension [5,6].
    [Show full text]
  • Center-Vortex Baryonic Area Law
    UCLA UCLA Previously Published Works Title Center-vortex baryonic area law Permalink https://escholarship.org/uc/item/3n3649xs Journal Physical Review D, 69(6) ISSN 0556-2821 Author Cornwall, J M Publication Date 2004-03-01 Peer reviewed eScholarship.org Powered by the California Digital Library University of California PHYSICAL REVIEW D 69, 065019 ͑2004͒ Relativistic center-vortex dynamics of a confining area law John M. Cornwall* Department of Physics and Astronomy, University of California, Los Angeles, California 90095, USA ͑Received 23 April 2003; published 26 March 2004͒ We offer a physicist’s proof that center-vortex theory requires the area in the ͑quenched͒ Wilson-loop area law to involve an extremal area. This means that, unlike in string-theory-inspired models of confining flux tubes, area-law dynamics is determined by integrating over Wilson loops only, not over surface fluctuations for a fixed loop. Fluctuations leading to perimeter-law corrections come from loop fluctuations as well as integra- tion over finite-thickness center-vortex collective coordinates. In dϭ3 ͑or dϭ2ϩ1) we exploit a contour form of the extremal area in isothermal ͑conformally flat metric on the surface͒ coordinates which is similar to d ϭ2 ͑or dϭ1ϩ1) QCD in many respects, except that there are both quartic and quadratic terms in the action. One major result is that at large angular momentum ᐉ in dϭ3ϩ1 the center-vortex extremal-area picture ␣ ␲ yields a linear Regge trajectory with a Regge slope–string tension product Ј(0)KF of 1/(2 ), which is the canonical Veneziano or string value. In a curious effect traceable to retardation, the quark kinetic terms in the ᐉ ϳ 1/2 action vanish relative to area-law terms in the large- limit, in which light-quark masses KF are negligible.
    [Show full text]
  • Center Vortices and Chiral Symmetry Breaking
    Die approbierte Originalversion dieser Dissertation ist an der Hauptbibliothek der Technischen Universität Wien aufgestellt (http://www.ub.tuwien.ac.at). The approved original version of this thesis is available at the main library of the Vienna University of Technology (http://www.ub.tuwien.ac.at/englweb/). asdf DISSERTATION Center Vortices and Chiral Symmetry Breaking ausgef¨uhrt zum Zwecke der Erlangung des akademischen Grades eines Doktors der technischen Wissenschaften unter der Leitung von Ao.Univ.Prof. Dr.techn. Manfried Faber Institutsnummer: E 141 Atominstitut eingereicht an der Technischen Universit¨at Wien Fakult¨at f¨ur Physik von Roman H¨ollwieser Matrikelnummer: 0127128 Am Brand 10, 2833 Bromberg Datum Unterschrift asdf Zusammenfassung Der Gegenstand dieser Dissertation ist die Untersuchung nicht-st¨orungstheoretischer Eigenschaften der Quanten Chromodynamik (QCD) mit Hilfe der Quantenfeldtheorie auf einem vierdimensionalen Raum-Zeit Gitter (Gitter QCD). Nach einer kurzen Einleitung wird in Abschnitt 2 das Vortexbild, ein Modell zur Erkl¨arung des Quarkeinschlusses (Confinement) in der QCD durch in sich geschlossene Farbwirbel (Vortices), die mit dem Zentrum der Eichgruppe verkn¨upft sind, vorgestellt. Im 3. Abschnitt werden seine Confinement-Eigenschaften im Rahmen der SU(2) Git- tereichtheorie mit (verbesserter) L¨uscher-Weisz Wirkung getestet. Danach soll das Vor- texmodell auf Ph¨anomene bez¨uglich chiraler Symmetrie analysiert werden, wobei hier die Relevanz des niedrigen Dirac Spektrums herangezogen wird. Das Atiyah-Singer Index Theorem erkl¨art topologische Ladung mit Hilfe des Indexes des Dirac Opera- tors w¨ahrend die Banks-Casher Formel die Dichte der nahen Dirac Moden dem chi- ralen Kondensat, einem Ordnungsparameter der chiralen Symmetriebrechung (SCSB), proportional setzt.
    [Show full text]
  • Heuristics of the Center Vortex Picture
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server A picture of the Yang-Mills deconfinement transition and its lattice verification1 M. Engelhardt2, K. Langfeld, H. Reinhardt3 and O. Tennert Institut f¨ur theoretische Physik, Universit¨at T¨ubingen Auf der Morgenstelle 14, 72076 T¨ubingen, Germany Abstract In the framework of the center vortex picture of confinement, the nature of the deconfining phase transition is studied. Using recently developed techniques which allow to associate a center vortex configuration with any given lattice gauge configuration, it is demonstrated that the confining phase is a phase in which vortices percolate, whereas the deconfined phase is a phase in which vortices cease to percolate if one considers an appropriate slice of space-time. Heuristics of the center vortex picture A discussion of the deconfinement transition in Yang-Mills theory presupposes a picture of the phenomenon of confinement. Conversely, any picture of confine- ment should be able to accomodate the deconfinement phase transition. The work presented here is concerned specifically with the so-called center vortex picture of confinement; this picture is based on the conjectured presence of center vor- tices in typical Yang-Mills gauge configurations. These vortices represent closed magnetic flux lines in three space dimensions, describing closed two-dimensional world-sheets in four space-time dimensions. Space-time in the following will al- ways be considered Euclidean. The magnetic flux represented by the vortices is furthermore quantized such that a Wilson loop linking vortex flux takes a value corresponding to a nontrivial center element of the gauge group.
    [Show full text]
  • Influence of Fermions on Vortices in SU(2)-QCD
    universe Article Influence of Fermions on Vortices in SU(2)-QCD Zeinab Dehghan 1 , Sedigheh Deldar 1, Manfried Faber 2,* , Rudolf Golubich 2 and Roman Höllwieser 3 1 Department of Physics, University of Tehran, Tehran 1439955961, Iran; [email protected] (Z.D.); [email protected] (S.D.) 2 Atominstitut, Technische Universität Wien, 1040 Wien, Austria; [email protected] 3 Department of Physics, Bergische Universität Wuppertal, 42119 Wuppertal, Germany; [email protected] * Correspondence: [email protected] Abstract: Gauge fields control the dynamics of fermions, and, in addition, a back reaction of fermions on the gauge field is expected. This back reaction is investigated within the vortex picture of the QCD vacuum. We show that the center vortex model reproduces the string tension of the full theory also in the presence of fermionic fields. Keywords: quantum chromodynamics; confinement; center vortex model; vacuum structure PACS: 11.15.Ha; 12.38.Gc 1. Introduction The QCD vacuum is highly nontrivial and has magnetic properties, as we have known since Savvidy’s article [1]. The QCD vacuum should explain the non-perturbative Citation: Dehghan, Z.; Deldar, S.; properties of QCD, including confinement [2] and chiral symmetry breaking [3]. Lattice Faber, M.; Golubich, R.; Höllwieser, R. QCD puts the means at our disposal to answer the question about the important degrees Influence of Fermions on Vortices in of freedom of this non-perturbative vacuum. In the center vortex picture [4–6], the QCD SU(2)-QCD. Universe 2021, 7, 130. vacuum is seen as a condensate of closed quantized magnetic flux tubes.
    [Show full text]