Contents. Goldstone Bosons in 3HeA Soft Modes Dynamics and Lie Algebra of Group G:


 Roy Alexander
 3 years ago
 Views:
Transcription
1
2 ... Vlll Contents 3. Textures and Supercurrents in Superfluid Phases of 3He 3.1. Textures, Gradient Energy and Rigidity 3.2. Why Superfuids are Superfluid 3.3. Superfluidity and Response to a Transverse Gauge Field 3.4. Nonpotential Superflow in 3HeA 3.5. Perpetuum Motion of the Aphase 3.6. Textural Energy and Supercurrent in 3HeA 3.7. Spin Soliton in 3HeA 3.8. Order Parameter Textures 3.9. Coherence Length and London Limit Disgyrations and Vortex. London Equations for the Orbital Texture Disgyrations and Vortex. Singularity in the Degeneracy Parameters Radial Disgyration. The Hard Core Structure Pure Vortices. The Hard Core Structure AB Interface. Symmetry and Structure Symmetry of the AB Interface and Boundary Conditions 4. Bose Excitations in Superfluid Phases of 3He Goldstone Bosons in 3HeA Soft Modes Dynamics and Lie Algebra of Group G: Spin Waves. Goldstone and QuasiGoldstone Nuclear Magnetic Resonance in 3HeA NMR on Textures in 3HeA Vacuum Symmetry H and Quantum Numbers of Bose and Fermi Excitations in 3HeA Bosonic Collective Modes in 3He and Irreducible Representations of Group H Bosonic Collective Modes in 3HeB Dynamics of the Goldstone Fields in 3HeB Superfluid Hydrodynamics in 3HeB Goldstone Bosons in 3HeB
3 Contents 5. Fermi Excitations in Superfluid Phases of 3He 5.1. BogoliubovNambu Matrix for Fermions in Paircorrelated Fermi Systems 5.2. Quasiparticles in Conventional Superconductors 5.3. Representation f and the Order P 5.4. Quasiparticle Spctrum in 5.5. Bogoliubov Hamiltonian for Quasiparticles in 3HeB vs. Dirac Hamiltonian for Electrons 5.6. Lorentz Symmetry as Combined Symmetry, View from 3HeB 5.7. Breaking of the Relative Lorentz Symmetry 5.8. Gap Nodes in the Quasiparticle Spectrum of 3HeA Class of Intermediate Superfluids 5.9. Combined Gauge Symmetry and Gap Nodes Stability of Gap Nodes in the Aphase Spectrum Near the Fermi Points and Relativistic Massless Particles Lefthanded and Righthanded Fermions Near the Fermi Points Spinorbit Waves and W Bosons Mass of the W Bosons is Zero in the BCS Theory of 3HeA Hidden Symmetry in the Aphase Origin of the W Boson Mass in 3HeA Gravitons in 3HeA Cosomological Term in the Einstein Equations, View from 3HeA ix Orbital Dynamics and Anomalies in Quantum Field Theory 6.1. Lie Algebra of Poisson Brackets for Aphase Orbital Dynamics 98 98
4 X Contents 6.2. Anomaly Cancellation as Lifshitz Transition 6.3. The Anomalyfree Equations for Orbital Dynamics 6.4. Phase Slippage Through the Dynamics of the Orbital Vector 6.5. Gap Nodes Contributions to the Orbital Dynamics 6.6. Anomaly in Orbital Dynamics and Chiral Anomaly 6.7. Spectrum of the Chiral Fermions in Magnetic Field 6.8. Anomalous Branch and Nonzero Density of States, Zero Charge Effect and Nonanalyticity of the Magnetic Energy of the Vacuum Nonanalytic London Energy of the 3He Vacuum ChiraI Anomaly and Nonconservationn of the Vacuum Current Dissipation in the Orbital Motion at Zero Temperature and Pair Creation in Electric Field in Particle Physics WessZumino Action for the Orbital Dynamics Internal Angular Momentum of the Aphase and the Mass of Photon Pair Creation by Accelerated Object and the Unruh Effect Topological Objects in Superfluid Phases of 3He Quantum Number and Topological Charge Topological and Symmetry Classification Schemes of Textures Halfquantum Vortex and Combined Invariance Topological Classification of the Linear Defects Topology of Linear Defects in the Aphase Unwinding of the Singularity in the Doubly Quantized Vortex Parity Breaking in the Continuous Vortex Topology of the Continuous Textures. Second Homotopy Group 7.9. Topological Phase Transition in Continuous Vortices
5 Contents xi Monopole and Boojum. Relative Homotopy Group Topology of Vortices and Disclinations in the Bphase Soliton Terminating on the Disclination in the Bphase Topological Confinement of the Defects in Superfluid 3He Stabilization of the VortexDisclination with the Solitonic Tail in the Rotating Vessel Spontaneous Symmetry Breaking in the 3He Vortices Compulsory and Spontaneous Symmetry Breaking in Inhomogeneous Vacuum Symmetry of Linear Defects Symmetry of Vortices in 3HeB The Most Symmetric Vortices in 3HeB Vortices Broken Parity in 3HeB Vortices Aphase Core of the 3HeB Vortex 8.7. Planar Phase vs. Aphase in the Core of the 3HeB Vortex 8.8. Broken Axisymmetry in 3HeB vortex. Molecule of Halfquantum Vortices 8.9. Physical Properties of the Vortices with Broken Symmetry QuasiTwoDimensional Superfluid 3He: Fractional Charge, Spin and Statistics Quasitwodimensional Objects in Superfluid 3He Superfluid Phases in Thin Films Generations of Fermions Symmetry and Internal Topology of Ground State Topological Invariant for the Fermi Point Topological Invariant in Terms of the Green s Function Topology of the Ground State of the 3He Film Adiabatical Process, Conservation of Topological Invariant and Diabolical Points
6 xii Contents Quantum Statistics of Solitons in the 3He Film and Orbital Ferromagnetism Spin Current QHE in Superfluid 3HeA Films Topological Quantization in Other Superfluid Phases of 3He Films Conclusion 207 References 211
Vortices at the AB phase boundary in superfluid 3 He
R. Hänninen Low Temperature Laboratory Helsinki University of Technology Finland Theory: E.V. Thuneberg G.E. Volovik Experiments: R. Blaauwgeers V.B. Eltsov A.P. Finne M. Krusius Outline:. Introduction
More informationSpontaneous symmetry breaking in particle physics: a case of cross fertilization
Spontaneous symmetry breaking in particle physics: a case of cross fertilization Yoichiro Nambu lecture presented by Giovanni JonaLasinio Nobel Lecture December 8, 2008 1 / 25 History repeats itself 1960
More informationMASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION)
MASTER OF SCIENCE IN PHYSICS Admission Requirements 1. Possession of a BS degree from a reputable institution or, for nonphysics majors, a GPA of 2.5 or better in at least 15 units in the following advanced
More informationDOCTOR OF PHILOSOPHY IN PHYSICS
DOCTOR OF PHILOSOPHY IN PHYSICS The Doctor of Philosophy in Physics program is designed to provide students with advanced graduate training in physics, which will prepare them for scientific careers in
More informationOrbital angular momentum and orbital dynamics: 3HeA and the Bose liquid
Orbital angular momentum and orbital dynamics: 3HeA and the Bose liquid G. E. Volovik and V. P. Mineev L. D. Landau Institute of Theoretical Physics, Academy of Sciences of the USSR (Submitted 3 March
More information1 Anomalies and the Standard Model
1 Anomalies and the Standard Model The GlashowWeinbergSalam model of the electroweak interactions has been very successful in explaining a wide range of experimental observations. The only major prediction
More informationSpinor Bose gases lecture outline
Spinor Bose gases lecture outline 1. Basic properties 2. Magnetic order of spinor BoseEinstein condensates 3. Imaging spin textures 4. Spinmixing dynamics We re here 5. Magnetic excitations Citizens,
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationCLASSIFICATION OF TOPOLOGICAL INSULATORS AND SUPERCONDUCTORS, RESPONSES AND QUANTUM ANOMALIES
CLASSIFICATION OF TOPOLOGICAL INSULATORS AND SUPERCONDUCTORS, RESPONSES AND QUANTUM ANOMALIES ANDREAS W.W. LUDWIG (UCSanta Barbara) work done in collaboration with: Shinsei Ryu (UCBerkeley) Andreas Schnyder
More information6 J  vector electric current density (A/m2 )
Determination of Antenna Radiation Fields Using Potential Functions Sources of Antenna Radiation Fields 6 J  vector electric current density (A/m2 ) M  vector magnetic current density (V/m 2 ) Some problems
More informationSpontaneous Symmetry Breaking
Spontaneous Symmetry Breaking in Particle Physics: a Case of Cross Fertilization Nobel Lecture, December 8, 2008 by Yoichiro Nambu *1 Department of Physics, Enrico Fermi Institute, University of Chicago,
More informationLocalization of scalar fields on Branes with an Asymmetric geometries in the bulk
Localization of scalar fields on Branes with an Asymmetric geometries in the bulk Vladimir A. Andrianov in collaboration with Alexandr A. Andrianov V.A.Fock Department of Theoretical Physics SanktPetersburg
More informationFrom Landau levels to quantum Hall effects
From Landau levels to quantum Hall effects by Bertrand I. Halperin, Harvard University Landau 100 Memorial Meeting Moscow, June 20, 2008 The Quantum Hall Effects Large set of peculiar phenomena in twodimensional
More informationConcepts in Theoretical Physics
Concepts in Theoretical Physics Lecture 6: Particle Physics David Tong e 2 The Structure of Things 4πc 1 137 e d ν u Four fundamental particles Repeated twice! va, 9608085, 9902033 Four fundamental forces
More informationPrecession of spin and Precession of a top
6. Classical Precession of the Angular Momentum Vector A classical bar magnet (Figure 11) may lie motionless at a certain orientation in a magnetic field. However, if the bar magnet possesses angular momentum,
More informationarxiv:hepth/0403037v6 4 Jul 2005
International Journal of Modern Physics A 20 (2005) 2795 2812 c World Scientific Publishing Company hepth/0403037 arxiv:hepth/0403037v6 4 Jul 2005 Emergent CPT violation from the splitting of Fermi points
More informationProf.M.Perucca CORSO DI APPROFONDIMENTO DI FISICA ATOMICA: (IIIINCONTRO) RISONANZA MAGNETICA NUCLEARE
Prof.M.Perucca CORSO DI APPROFONDIMENTO DI FISICA ATOMICA: (IIIINCONTRO) RISONANZA MAGNETICA NUCLEARE SUMMARY (I/II) Angular momentum and the spinning gyroscope stationary state equation Magnetic dipole
More information1D 3D 1D 3D. is called eigenstate or state function. When an operator act on a state, it can be written as
Chapter 3 (Lecture 45) Postulates of Quantum Mechanics Now we turn to an application of the preceding material, and move into the foundations of quantum mechanics. Quantum mechanics is based on a series
More informationThe Higgs Boson. Linac08 Victoria BC, Canada CANADA S NATIONAL LABORATORY FOR PARTICLE AND NUCLEAR PHYSICS
CANADA S NATIONAL LABORATORY FOR PARTICLE AND NUCLEAR PHYSICS Owned and operated as a joint venture by a consortium of Canadian universities via a contribution through the National Research Council Canada
More informationOrbital Dynamics coupled with JahnTeller phonons in Strongly Correlated Electron System
The 5 th Scienceweb GCOE International Symposium 1 Orbital Dynamics coupled with JahnTeller phonons in Strongly Correlated Electron System Department of Physics, Tohoku University Joji Nasu In collaboration
More informationElectrical Conductivity
Advanced Materials Science  Lab Intermediate Physics University of Ulm Solid State Physics Department Electrical Conductivity Translated by MichaelStefan Rill January 20, 2003 CONTENTS 1 Contents 1 Introduction
More informationSTRING THEORY: Past, Present, and Future
STRING THEORY: Past, Present, and Future John H. Schwarz Simons Center March 25, 2014 1 OUTLINE I) Early History and Basic Concepts II) String Theory for Unification III) Superstring Revolutions IV) Remaining
More informationTheoretical Particle Physics FYTN04: Oral Exam Questions, version ht15
Theoretical Particle Physics FYTN04: Oral Exam Questions, version ht15 Examples of The questions are roughly ordered by chapter but are often connected across the different chapters. Ordering is as in
More informationNMR SPECTROSCOPY. Basic Principles, Concepts, and Applications in Chemistry. Harald Günther University of Siegen, Siegen, Germany.
NMR SPECTROSCOPY Basic Principles, Concepts, and Applications in Chemistry Harald Günther University of Siegen, Siegen, Germany Second Edition Translated by Harald Günther JOHN WILEY & SONS Chichester
More informationarxiv:condmat/9301024v1 20 Jan 1993 ABSTRACT
Anyons as Dirac Strings, the A x = 0 Gauge LPTB 931 John McCabe Laboratoire de Physique Théorique, 1 Université Bordeaux I 19 rue du Solarium, 33175 Gradignan FRANCE arxiv:condmat/930104v1 0 Jan 1993
More informationSubAtomic Physics Nuclear Physics
SubAtomic Physics Nuclear Physics Lecture 4 Main points of Lecture 3 Strong and coulomb interaction processes conserve angular momentum and parity External properties 1) Charge number of protons (ze) 2)
More informationQuantum Mechanics and Representation Theory
Quantum Mechanics and Representation Theory Peter Woit Columbia University Texas Tech, November 21 2013 Peter Woit (Columbia University) Quantum Mechanics and Representation Theory November 2013 1 / 30
More informationExperimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator Chang et al., Science 340, 167 (2013). Joseph Hlevyack, Hu Jin, Mazin Khader, Edward Kim Outline: Introduction:
More informationWhy the high lying glueball does not mix with the neighbouring f 0. Abstract
Why the high lying glueball does not mix with the neighbouring f 0. L. Ya. Glozman Institute for Theoretical Physics, University of Graz, Universitätsplatz 5, A800 Graz, Austria Abstract Chiral symmetry
More informationAssessment Plan for Learning Outcomes for BA/BS in Physics
Department of Physics and Astronomy Goals and Learning Outcomes 1. Students know basic physics principles [BS, BA, MS] 1.1 Students can demonstrate an understanding of Newton s laws 1.2 Students can demonstrate
More informationAppendix E  Elements of Quantum Mechanics
1 Appendix E  Elements of Quantum Mechanics Quantum mechanics provides a correct description of phenomena on the atomic or sub atomic scale, where the ideas of classical mechanics are not generally applicable.
More informationElectrical current carried by neutral quasiparticles
PHYSICAL REVIEW B, VOLUME 64, 235113 Electrical current carried by neutral quasiparticles Chetan Nayak, 1 Kirill Shtengel, 2 Dror Orgad, 1 Matthew P. A. Fisher, 3 and S. M. Girvin 3,4 1 Department of Physics
More information3. Derive the partition function for the ideal monoatomic gas. Use Boltzmann statistics, and a quantum mechanical model for the gas.
Tentamen i Statistisk Fysik I den tjugosjunde februari 2009, under tiden 9.0015.00. Lärare: Ingemar Bengtsson. Hjälpmedel: Penna, suddgummi och linjal. Bedömning: 3 poäng/uppgift. Betyg: 03 = F, 46
More informationGauge theories and the standard model of elementary particle physics
Gauge theories and the standard model of elementary particle physics Mark Hamilton 21st July 2014 1 / 35 Table of contents 1 The standard model 2 3 2 / 35 The standard model The standard model is the most
More informationGravity and running coupling constants
Gravity and running coupling constants 1) Motivation and history 2) Brief review of running couplings 3) Gravity as an effective field theory 4) Running couplings in effective field theory 5) Summary 6)
More informationFrom Einstein to KleinGordon Quantum Mechanics and Relativity
From Einstein to KleinGordon Quantum Mechanics and Relativity Aline Ribeiro Department of Mathematics University of Toronto March 24, 2002 Abstract We study the development from Einstein s relativistic
More informationChapter 22 The Hamiltonian and Lagrangian densities. from my book: Understanding Relativistic Quantum Field Theory. Hans de Vries
Chapter 22 The Hamiltonian and Lagrangian densities from my book: Understanding Relativistic Quantum Field Theory Hans de Vries January 2, 2009 2 Chapter Contents 22 The Hamiltonian and Lagrangian densities
More informationPHYS 1624 University Physics I. PHYS 2644 University Physics II
PHYS 1624 Physics I An introduction to mechanics, heat, and wave motion. This is a calculus based course for Scientists and Engineers. 4 hours (3 lecture/3 lab) Prerequisites: Credit for MATH 2413 (Calculus
More informationInstability, dispersion management, and pattern formation in the superfluid flow of a BEC in a cylindrical waveguide
Instability, dispersion management, and pattern formation in the superfluid flow of a BEC in a cylindrical waveguide Michele Modugno LENS & Dipartimento di Fisica, Università di Firenze, Italy Workshop
More information3. Open Strings and DBranes
3. Open Strings and DBranes In this section we discuss the dynamics of open strings. Clearly their distinguishing feature is the existence of two end points. Our goal is to understand the effect of these
More informationThe force equation of quantum mechanics.
The force equation of quantum mechanics. by M. W. Evans, Civil List and Guild of Graduates, University of Wales, (www.webarchive.org.uk, www.aias.us,, www.atomicprecision.com, www.upitec.org, www.et3m.net)
More information2, 8, 20, 28, 50, 82, 126.
Chapter 5 Nuclear Shell Model 5.1 Magic Numbers The binding energies predicted by the Liquid Drop Model underestimate the actual binding energies of magic nuclei for which either the number of neutrons
More information2. Spin Chemistry and the Vector Model
2. Spin Chemistry and the Vector Model The story of magnetic resonance spectroscopy and intersystem crossing is essentially a choreography of the twisting motion which causes reorientation or rephasing
More informationIntroduction to SME and Scattering Theory. Don Colladay. New College of Florida Sarasota, FL, 34243, U.S.A.
June 2012 Introduction to SME and Scattering Theory Don Colladay New College of Florida Sarasota, FL, 34243, U.S.A. This lecture was given at the IUCSS summer school during June of 2012. It contains a
More informationLecture 13. Magnetic Field, Magnetic Forces on Moving Charges. Outline:
Lecture 13. Magnetic Field, Magnetic Forces on Moving Charges. Outline: Intro to Magnetostatics. Magnetic Field Flux, Absence of Magnetic Monopoles. Force on charges moving in magnetic field. 1 Intro to
More informationStatistical Physics, Part 2 by E. M. Lifshitz and L. P. Pitaevskii (volume 9 of Landau and Lifshitz, Course of Theoretical Physics).
Fermi liquids The electric properties of most metals can be well understood from treating the electrons as noninteracting. This free electron model describes the electrons in the outermost shell of the
More informationL5. P1. Lecture 5. Solids. The free electron gas
Lecture 5 Page 1 Lecture 5 L5. P1 Solids The free electron gas In a solid state, a few loosely bound valence (outermost and not in completely filled shells) elections become detached from atoms and move
More informationGRAPHENE: A NEW STAR IN MATERIAL SCIENCE
GRAPHENE: A NEW STAR IN MATERIAL SCIENCE S. Sahoo 1 & A. K. Dutta 2 Department of Physics, National Institute of Technology Durgapur713209, West Bengal, India. 1 Email: sukadevsahoo@yahoo.com 2 Email:
More information(Most of the material presented in this chapter is taken from Thornton and Marion, Chap. 7)
Chapter 4. Lagrangian Dynamics (Most of the material presented in this chapter is taken from Thornton and Marion, Chap. 7 4.1 Important Notes on Notation In this chapter, unless otherwise stated, the following
More informationChapter 9 Unitary Groups and SU(N)
Chapter 9 Unitary Groups and SU(N) The irreducible representations of SO(3) are appropriate for describing the degeneracies of states of quantum mechanical systems which have rotational symmetry in three
More informationLecture 2: Semiconductors: Introduction
Lecture 2: Semiconductors: Introduction Contents 1 Introduction 1 2 Band formation in semiconductors 2 3 Classification of semiconductors 5 4 Electron effective mass 10 1 Introduction Metals have electrical
More informationThreegeneration models in heterotic asymmetric orbifolds
Threegeneration models in heterotic asymmetric orbifolds Shogo Kuwakino (Chung Yuan Christian U., Taiwan) Based on arxiv:1304.5621 [hepth] and 1311.4687 [hepth] Collaborator : Florian Beye (Nagoya university)
More informationPerfect Fluidity in Cold Atomic Gases?
Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 2 Hydrodynamics Longwavelength, lowfrequency dynamics of conserved or spontaneoulsy broken symmetry variables.
More informationPerfect Fluids: From Nano to Tera
Perfect Fluids: From Nano to Tera Thomas Schaefer North Carolina State University 1 2 Perfect Fluids sqgp (T=180 MeV) Neutron Matter (T=1 MeV) Trapped Atoms (T=0.1 nev) 3 Hydrodynamics Longwavelength,
More informationSpecial Relativity and Electromagnetism Yannis PAPAPHILIPPOU CERN
Special Relativity and Electromagnetism Yannis PAPAPHILIPPOU CERN United States Particle Accelerator School, University of California  Santa Cruz, Santa Rosa, CA 14 th 18 th January 2008 1 Outline Notions
More informationPHY411. PROBLEM SET 3
PHY411. PROBLEM SET 3 1. Conserved Quantities; the RungeLenz Vector The Hamiltonian for the Kepler system is H(r, p) = p2 2 GM r where p is momentum, L is angular momentum per unit mass, and r is the
More informationAMPLIFICATION OF ATOMIC WAVES BY STIMULATED EMISSION OF ATOMS. Christian J. Borde
AMPLIFIATION OF ATOMI WAVES BY STIMULATED EMISSION OF ATOMS hristian J. Borde Laboratoire de Physique des Lasers, NRS/URA 8, Universite ParisNord, Villetaneuse, France. INTRODUTION: The recent development
More informationRighthanded neutrinos
Righthanded neutrinos O. Steinkamp, N. Serra, B. Storaci Flavor physics Neutrino oscillations: Last Lecture Interpretation of neutrino mixing in two and three neutrino family formalism Neutrino oscillation
More informationRules for this test. Physics 222, Winter 2012 Final Exam April 16, 2012 Instructor: Scott Bergeson
Physics 222, Winter 2012 Final Exam April 16, 2012 Instructor: Scott Bergeson Rules for this test 1. This test is open book and open notes, including our class notes page online, and your homework solutions.
More informationarxiv:1111.4354v2 [physics.accph] 27 Oct 2014
Theory of Electromagnetic Fields Andrzej Wolski University of Liverpool, and the Cockcroft Institute, UK arxiv:1111.4354v2 [physics.accph] 27 Oct 2014 Abstract We discuss the theory of electromagnetic
More informationLaws of Motion and Conservation Laws
Laws of Motion and Conservation Laws The first astrophysics we ll consider will be gravity, which we ll address in the next class. First, though, we need to set the stage by talking about some of the basic
More informationNUCLEAR MAGNETIC RESONANCE SPECTROSCOPY
NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY PRINCIPLE AND APPLICATION IN STRUCTURE ELUCIDATION Professor S. SANKARARAMAN Department of Chemistry Indian Institute of Technology Madras Chennai 600 036 sanka@iitm.ac.in
More informationThe Higgs Particle, Pivot of the Standard Model of the Subatomic Particles
The Higgs Particle, Pivot of the Standard Model of the Subatomic Particles Utrecht University Gerard t Hooft, Public Lecture, Sendai, April 24, 2015 CERN European Center for Nuclear Research LHC Large
More informationNeutron Star Structure
Neutron Star Structure We now enter the study of neutron stars. Like black holes, neutron stars are one of the three possible endpoints of stellar evolution (the remaining one being white dwarfs). Also
More informationThe Quantum Harmonic Oscillator Stephen Webb
The Quantum Harmonic Oscillator Stephen Webb The Importance of the Harmonic Oscillator The quantum harmonic oscillator holds a unique importance in quantum mechanics, as it is both one of the few problems
More informationPerfect Fluidity in Cold Atomic Gases?
Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Hydrodynamics Longwavelength, lowfrequency dynamics of conserved or spontaneoulsy broken symmetry variables τ
More informationSyllabus for Chem 359: Atomic and Molecular Spectroscopy
Syllabus for Chem 359: Atomic and Molecular Spectroscopy Instructors: Dr. Reinhard Schweitzer Stenner and Ms. Siobhan E. Toal Of#ice: Disque 605/Disque 306 Tel: (215) 8952268 Email: rschweitzer stenner@drexel.edu
More informationSubatomic Physics: Particle Physics Lecture 4. Quantum ElectroDynamics & Feynman Diagrams. Antimatter. Virtual Particles. Yukawa Potential for QED
Ψ e (r, t) exp i/ (E)(t) (p) (r) Subatomic Physics: Particle Physics Lecture Quantum ElectroDynamics & Feynman Diagrams Antimatter Feynman Diagram and Feynman Rules Quantum description of electromagnetism
More informationPhysics Department, Southampton University Highfield, Southampton, S09 5NH, U.K.
\ \ IFT Instituto de Física Teórica Universidade Estadual Paulista July/92 IFTP.025/92 LEPTON MASSES IN AN SU(Z) L U(1) N GAUGE MODEL R. Foot a, O.F. Hernandez ", F. Pisano e, and V. Pleitez 0 Physics
More informationTYPE II SUPERCONDUCTORS AND THE VORTEX LATTICE
TYPE II SUPERCONDUCTORS AND THE VORTEX LATTICE Nobel Lecture, December 8, 2003 by Alexei A. Abrikosov Materials Science Division, Argonne National Laboratory, 9700 South Cass Ave., Argonne, IL 60439, USA.
More informationPX408: Relativistic Quantum Mechanics
January 2016 PX408: Relativistic Quantum Mechanics Tim Gershon (T.J.Gershon@warwick.ac.uk) Handout 1: Revision & Notation Relativistic quantum mechanics, as its name implies, can be thought of as the bringing
More informationState of Stress at Point
State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,
More informationIndiana's Academic Standards 2010 ICP Indiana's Academic Standards 2016 ICP. map) that describe the relationship acceleration, velocity and distance.
.1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations
More informationNeutron stars as laboratories for exotic physics
Ian Jones Neutron stars as laboratories for exotic physics 1/20 Neutron stars as laboratories for exotic physics Ian Jones D.I.Jones@soton.ac.uk General Relativity Group, Southampton University Context
More informationPerfect Fluidity in Cold Atomic Gases?
Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Elliptic Flow Hydrodynamic expansion converts coordinate space anisotropy to momentum space anisotropy Anisotropy
More informationThree Pictures of Quantum Mechanics. Thomas R. Shafer April 17, 2009
Three Pictures of Quantum Mechanics Thomas R. Shafer April 17, 2009 Outline of the Talk Brief review of (or introduction to) quantum mechanics. 3 different viewpoints on calculation. Schrödinger, Heisenberg,
More informationNDSU Department of Physics. Graduate Student Handbook
NDSU Department of Physics Graduate Student Handbook Department of Physics North Dakota State University Fargo, ND 581086050 History Draft: August 24, 2014 Table of Contents 1. Contact 2 2. Graduate Program
More informationDifferential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation
Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of
More informationAn Introduction of Topological Orders
An Introduction of Topological Orders XiaoGang Wen Dept. of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 http://dao.mit.edu/ wen Abstract One of most fundamental issues
More informationFeynman diagrams. 1 Aim of the game 2
Feynman diagrams Contents 1 Aim of the game 2 2 Rules 2 2.1 Vertices................................ 3 2.2 Antiparticles............................. 3 2.3 Distinct diagrams...........................
More informationSolid State Theory. (Theorie der kondensierten Materie) Wintersemester 2015/16
Martin Eckstein Solid State Theory (Theorie der kondensierten Materie) Wintersemester 2015/16 MaxPlanck Research Departement for Structural Dynamics, CFEL Desy, Bldg. 99, Rm. 02.001 Luruper Chaussee 149
More informationQuantum Field Theory and Representation Theory
Quantum Field Theory and Representation Theory Peter Woit woit@math.columbia.edu Department of Mathematics Columbia University Quantum Field Theory and Representation Theory p.1 Outline of the talk Quantum
More informationParton models of 3D fractional topological insulators
Parton models of 3D fractional topological insulators Joseph Maciejko Princeton Center for Theoretical Science Princeton University October 7, 2011 topomat11 @ KITP Collaborators: X. L. Qi and S. C. Zhang
More informationParticle Physics. Michaelmas Term 2011 Prof Mark Thomson. Handout 7 : Symmetries and the Quark Model. Introduction/Aims
Particle Physics Michaelmas Term 2011 Prof Mark Thomson Handout 7 : Symmetries and the Quark Model Prof. M.A. Thomson Michaelmas 2011 206 Introduction/Aims Symmetries play a central role in particle physics;
More informationWAVES AND FIELDS IN INHOMOGENEOUS MEDIA
WAVES AND FIELDS IN INHOMOGENEOUS MEDIA WENG CHO CHEW UNIVERSITY OF ILLINOIS URBANACHAMPAIGN IEEE PRESS Series on Electromagnetic Waves Donald G. Dudley, Series Editor IEEE Antennas and Propagation Society,
More informationContinuous Groups, Lie Groups, and Lie Algebras
Chapter 7 Continuous Groups, Lie Groups, and Lie Algebras Zeno was concerned with three problems... These are the problem of the infinitesimal, the infinite, and continuity... Bertrand Russell The groups
More informationNMR and IR spectra & vibrational analysis
Lab 5: NMR and IR spectra & vibrational analysis A brief theoretical background 1 Some of the available chemical quantum methods for calculating NMR chemical shifts are based on the HartreeFock selfconsistent
More informationLecture 5 Motion of a charged particle in a magnetic field
Lecture 5 Motion of a charged particle in a magnetic field Charged particle in a magnetic field: Outline 1 Canonical quantization: lessons from classical dynamics 2 Quantum mechanics of a particle in a
More informationCollege of Arts and Sciences
Note: It is assumed that all prerequisites include, in addition to any specific course listed, the phrase or equivalent, or consent of instructor. 105 SICS AND ASTRONOMY TODAY. (1) This course is intended
More informationLecture 1: Microscopic Theory of Radiation
253a: QFT Fall 2009 Matthew Schwartz Lecture : Microscopic Theory of Radiation Blackbody Radiation Quantum Mechanics began on October 9, 900 with Max Planck s explanation of the blackbody radiation spectrum.
More informationElectric Dipole moments as probes of physics beyond the Standard Model
Electric Dipole moments as probes of physics beyond the Standard Model K. V. P. Latha NonAccelerator Particle Physics Group Indian Institute of Astrophysics Plan of the Talk Parity (P) and Timereversal
More informationChapter 18: The Structure of the Atom
Chapter 18: The Structure of the Atom 1. For most elements, an atom has A. no neutrons in the nucleus. B. more protons than electrons. C. less neutrons than electrons. D. just as many electrons as protons.
More informationSpontaneous Magnetic Flux Induced by Ferromagnetic πjunctions
Spontaneous Magnetic Flux Induced by Ferromagnetic πjunctions Φ 0 /2 S π S FM Dissertation zur Erlangung des Doktorgrades der Naturwissenschaften (Dr. rer. nat.) der naturwissenschaftlichen Fakultät II
More informationSCATTERING CROSS SECTIONS AND LORENTZ VIOLATION DON COLLADAY
SCATTERING CROSS SECTIONS AND LORENTZ VIOLATION DON COLLADAY New College of Florida, 5700 Tamiami Trail, Sarasota, FL 34243, USA Email: colladay@sar.usf.edu To date, a significant effort has been made
More informationChapter 4. Magnetic Materials and Circuits
Chapter 4 Magnetic Materials and Circuits Objectives List six characteristics of magnetic field. Understand the righthand rule for current and magnetic fluxes. Define magnetic flux, flux density, magnetomotive
More informationSpringerVerlag Berlin Heidelberg GmbH
W. Greiner 1. Reinhardt FIELD QUANTIZATION SpringerVerlag Berlin Heidelberg GmbH Greiner Quantum Mechanics An Introduction 3rd Edition Greiner Quantum Mechanics Special Chapters Greiner. MUller Quantum
More informationDynamics of Rotational Motion
Chapter 10 Dynamics of Rotational Motion PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 5_31_2012 Goals for Chapter
More informationEðlisfræði 2, vor 2007
[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 28. Sources of Magnetic Field Assignment is due at 2:00am on Wednesday, March 7, 2007 Credit for problems submitted late will decrease to 0% after the deadline
More informationIntroduction: Measurements in Particle Physics
Subatomic Physics: Particle Physics Lecture 2 Introduction to Measurements in Particle Physics Measuring properties of particles and interactions Particle quantum numbers and conservation laws Review of
More informationBasic Concepts in Nuclear Physics
Basic Concepts in Nuclear Physics Paolo Finelli Corso di Teoria delle Forze Nucleari 2011 Literature/Bibliography Some useful texts are available at the Library: Wong, Nuclear Physics Krane, Introductory
More information