What is macro? self-organized structures in physical systems
|
|
- Iris Gibbs
- 5 years ago
- Views:
Transcription
1 What is macro? self-organized structures in physical systems Z. Yoshida U. Tokyo Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 1 / 15
2 Outline Self-organization without blueprints Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 2 / 15
3 Outline Self-organization without blueprints Creation by space (not by matter) Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 2 / 15
4 Outline Self-organization without blueprints Creation by space (not by matter) Topological constraints and foliation Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 2 / 15
5 Outline Self-organization without blueprints Creation by space (not by matter) Topological constraints and foliation Macro-hierarchy as leaves in phase space Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 2 / 15
6 Outline Self-organization without blueprints Creation by space (not by matter) Topological constraints and foliation Macro-hierarchy as leaves in phase space Self-organization of vortexes Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 2 / 15
7 Outline Self-organization without blueprints Creation by space (not by matter) Topological constraints and foliation Macro-hierarchy as leaves in phase space Self-organization of vortexes Cluster vs Vortex Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 2 / 15
8 Outline Self-organization without blueprints Creation by space (not by matter) Topological constraints and foliation Macro-hierarchy as leaves in phase space Self-organization of vortexes Cluster vs Vortex Self-organized confinement in magnetosphere Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 2 / 15
9 Outline Self-organization without blueprints Creation by space (not by matter) Topological constraints and foliation Macro-hierarchy as leaves in phase space Self-organization of vortexes Cluster vs Vortex Self-organized confinement in magnetosphere Possibility of advanced fusion Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 2 / 15
10 Self-organization with blueprints Figure: Hierarchical structures are programed to emerge by gene. (The picture of cell is by Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 3 / 15
11 Self-organization without blueprints Figure: Self-organization in physical systems: Vortexes are chiral structures spontaneously created without programs. The picture of M51 spiral galaxy is by K. Okano; rt6k-okn/galaxy/m51aom.jpg Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 4 / 15
12 Self-organization without blueprints Figure: Self-organization in physical systems: Vortexes are chiral structures spontaneously created without programs. The picture of M51 spiral galaxy is by K. Okano; rt6k-okn/galaxy/m51aom.jpg Elements are just simple. The magic is played by space-time. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 4 / 15
13 Physicist s view of pendulum Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 5 / 15
14 Physicist s view of pendulum Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 5 / 15
15 Physicist s view of pendulum Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 5 / 15
16 Duality of matter and space-time Why chiral? Symmetry breaking in the matter Symmetry breaking in the space Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 6 / 15
17 Duality of matter and space-time Why chiral? Symmetry breaking in the matter Symmetry breaking in the space Here, we put the rattle back into the perspective of skewed space, and explain the chirality as the consequence of the distorted geometry. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 6 / 15
18 Duality of matter and space-time Why chiral? Symmetry breaking in the matter Symmetry breaking in the space Here, we put the rattle back into the perspective of skewed space, and explain the chirality as the consequence of the distorted geometry. We start with the Moffatt-Tokieda equation [Proc. Royal Soc. Edinburgh 138A (2008), 361]. We cast it into a Hamiltonian formalism; the underlying Lie algebra is of Bianchi Type VI. The chirality of the rattleback motion is caused by the skewed space in which the rattle back lives. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 6 / 15
19 Moffatt-Tokieda equation of rattle back The governing equation of P= pitching, R= rolling, and S= spin is P R P d R = λp R. (1) dt S 0 S We assume that λ is a positive constant number. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 7 / 15
20 Moffatt-Tokieda equation of rattle back The governing equation of P= pitching, R= rolling, and S= spin is P R P d R = λp R. (1) dt S 0 S We assume that λ is a positive constant number t 0.4 Figure: Typical solution of spin reversal: Reproduced from Fig. 1 of Moffatt-Tokieda (2008) Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 7 / 15
21 Casimir invariant and the orbits The rattle back motion is the cross-section of the energy H := 1 2 Z 2 = 1 ( P 2 + R 2 + S 2) 2 and the Casimir invariant C := PR λ. (2) Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 8 / 15
22 Figure: The slice of the energy contour (H = constant) by a distorted knife (the Casimir leaf) yields a skewed orbit. (ZY, T. Tokieda and J.P. Morrison, 2016 IUTAM Symposium, Venice, Italy) Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 8 / 15 Casimir invariant and the orbits The rattle back motion is the cross-section of the energy H := 1 2 Z 2 = 1 ( P 2 + R 2 + S 2) 2 and the Casimir invariant C := PR λ. (2)
23 What is macro? Micro = canonical Macro = noncanonical foliation = topological constraints Figure: When the dynamics is topologically constrained to a skewed leaf, the effective energy may have complex distribution, branching out variety of structures. (Fig. 1 of Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 9 / 15
24 Self-organization of vortexes Two different types of naturally-made structures: Clusters: star, nebula, Debye shield, etc. Vortexes: spiral galaxy, magnetosphere, typhoon, tornado, etc. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 10 / 15
25 Self-organization of vortexes Two different types of naturally-made structures: Clusters: star, nebula, Debye shield, etc. Vortexes: spiral galaxy, magnetosphere, typhoon, tornado, etc. Two-different types of interactions: Forces due to energy: gravity (Newtonian), electrostatic force, etc. Forces due to space-time: magnetic force, Coriolis force, etc. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 10 / 15
26 Creation by topological constraints How can magnetic field confine a plasma, despite the fact that f e E/k BT? Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 11 / 15
27 Creation by topological constraints How can magnetic field confine a plasma, despite the fact that f e E/k BT? Confinement occurs on a macro hierarchy. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 11 / 15
28 Creation by topological constraints How can magnetic field confine a plasma, despite the fact that f e E/k BT? Confinement occurs on a macro hierarchy. Magnetized particles = quasi-particle involving micro degree of freedom. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 11 / 15
29 Creation by topological constraints How can magnetic field confine a plasma, despite the fact that f e E/k BT? Confinement occurs on a macro hierarchy. Magnetized particles = quasi-particle involving micro degree of freedom. Quasi-particles reside on a leaf of adiabatic invariants. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 11 / 15
30 Boltzmann distribution on a leaf Quasi-particles reside on a leaf of adiabatic invariants. Boltzmann distribution of quasi-particles maximizes entropy with respect to the invariant measure of the symplectic leaf. Figure: (left) Boltzmann distribution on the leaf of µ (magnetic moment). (right) Boltzmann distribution on the leaf of µ and J (bounce action). (Fig. 1 of ZY & S.M. Mahajan, PETP 2014, 073J01) Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 12 / 15
31 Experimental proof of the self-organized magnetosphere Figure: (left) Theoretical model of planetary (Jovian) magnetosphere. (right) RT-1 laboratory magnetosphere at The University of Tokyo. ( Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 13 / 15
32 Problems in the frontier Non-integrable topological constraints: singularities in Poisson algebra non-holonomic constraints Fragility of topological constraints: topological evolution turbulence Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 14 / 15
33 Problems in the frontier Non-integrable topological constraints: singularities in Poisson algebra non-holonomic constraints Fragility of topological constraints: topological evolution turbulence Application of the self-organizing dynamics: advanced fusion (plasma confinement for D- 3He fusion energy) anti-matter plasma (e-p plasma,, etc.) Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 14 / 15
34 Summary Macro can be different from the simple sum (direct product) of micros, if topological constraints foliates the phase space. Macro hierarchy is identified as leaves of adiabatic invariants. The Casimir invariants of Hamiltonian systems may be regarded as adiabatic invariants, Skewness of Casimir leaves yields non-trivial structures. Z. Yoshida (U. Tokyo) Self-organization in macro systems 2016/05/24 15 / 15
Hamiltonian and Non-Hamiltonian Reductions of Charged Particle Dynamics: Diffusion and Self-Organization
NNP2017 11 th July 2017 Lawrence University Hamiltonian and Non-Hamiltonian Reductions of Charged Particle Dynamics: Diffusion and Self-Organization N. Sato and Z. Yoshida Graduate School of Frontier Sciences
More informationarxiv: v1 [math-ph] 29 Sep 2016
A Prototype Rattleback Model a Lie-Poisson Bianchi Type VI System with Chirality arxiv:1609.093v1 [math-ph] 9 Sep 016 Z Yoshida 1, T Tokieda, and P J Morrison 3 1 Graduate School of Frontier Sciences,
More informationarxiv: v2 [math-ph] 5 Jul 2017
Rattleback: a model of how geometric singularity induces dynamic chirality Z. Yoshida a, T. Tokieda b, P.J. Morrison c a Department of Advanced Energy, University of Tokyo, Kashiwa, Chiba 77-8561, Japan
More informationConfinement of toroidal non-neutral plasma
10th International Workshop on Non-neutral Plasmas 28 August 2012, Greifswald, Germany 1/20 Confinement of toroidal non-neutral plasma in magnetic dipole RT-1: Magnetospheric plasma experiment Visualized
More informationStability Subject to Dynamical Accessibility
Stability Subject to Dynamical Accessibility P. J. Morrison Department of Physics and Institute for Fusion Studies The University of Texas at Austin morrison@physics.utexas.edu http://www.ph.utexas.edu/
More informationPRINCIPLES OF PHYSICS. \Hp. Ni Jun TSINGHUA. Physics. From Quantum Field Theory. to Classical Mechanics. World Scientific. Vol.2. Report and Review in
LONDON BEIJING HONG TSINGHUA Report and Review in Physics Vol2 PRINCIPLES OF PHYSICS From Quantum Field Theory to Classical Mechanics Ni Jun Tsinghua University, China NEW JERSEY \Hp SINGAPORE World Scientific
More informationHamilton description of plasmas and other models of matter: structure and applications I
Hamilton description of plasmas and other models of matter: structure and applications I P. J. Morrison Department of Physics and Institute for Fusion Studies The University of Texas at Austin morrison@physics.utexas.edu
More informationLecture I: Constrained Hamiltonian systems
Lecture I: Constrained Hamiltonian systems (Courses in canonical gravity) Yaser Tavakoli December 15, 2014 1 Introduction In canonical formulation of general relativity, geometry of space-time is given
More informationElectrical Transport in Nanoscale Systems
Electrical Transport in Nanoscale Systems Description This book provides an in-depth description of transport phenomena relevant to systems of nanoscale dimensions. The different viewpoints and theoretical
More informationQuantum Field Theory. Kerson Huang. Second, Revised, and Enlarged Edition WILEY- VCH. From Operators to Path Integrals
Kerson Huang Quantum Field Theory From Operators to Path Integrals Second, Revised, and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA I vh Contents Preface XIII 1 Introducing Quantum Fields
More informationGyrokinetic simulations of magnetic fusion plasmas
Gyrokinetic simulations of magnetic fusion plasmas Tutorial 2 Virginie Grandgirard CEA/DSM/IRFM, Association Euratom-CEA, Cadarache, 13108 St Paul-lez-Durance, France. email: virginie.grandgirard@cea.fr
More informationScaling laws for planetary dynamos driven by helical waves
Scaling laws for planetary dynamos driven by helical waves P. A. Davidson A. Ranjan Cambridge What keeps planetary magnetic fields alive? (Earth, Mercury, Gas giants) Two ingredients of the early theories:
More information= 0. = q i., q i = E
Summary of the Above Newton s second law: d 2 r dt 2 = Φ( r) Complicated vector arithmetic & coordinate system dependence Lagrangian Formalism: L q i d dt ( L q i ) = 0 n second-order differential equations
More informationMATHEMATICAL STRUCTURES IN CONTINUOUS DYNAMICAL SYSTEMS
MATHEMATICAL STRUCTURES IN CONTINUOUS DYNAMICAL SYSTEMS Poisson Systems and complete integrability with applications from Fluid Dynamics E. van Groesen Dept. of Applied Mathematics University oftwente
More informationLectures on basic plasma physics: Hamiltonian mechanics of charged particle motion
Lectures on basic plasma physics: Hamiltonian mechanics of charged particle motion Department of applied physics, Aalto University March 8, 2016 Hamiltonian versus Newtonian mechanics Newtonian mechanics:
More informationDeconfined Quantum Critical Points
Deconfined Quantum Critical Points Outline: with T. Senthil, Bangalore A. Vishwanath, UCB S. Sachdev, Yale L. Balents, UCSB conventional quantum critical points Landau paradigm Seeking a new paradigm -
More informationPentahedral Volume, Chaos, and Quantum Gravity
Pentahedral Volume, Chaos, and Quantum Gravity Hal Haggard May 30, 2012 Volume Polyhedral Volume (Bianchi, Doná and Speziale): ˆV Pol = The volume of a quantum polyhedron Outline 1 Pentahedral Volume 2
More informationNon-associative Deformations of Geometry in Double Field Theory
Non-associative Deformations of Geometry in Double Field Theory Michael Fuchs Workshop Frontiers in String Phenomenology based on JHEP 04(2014)141 or arxiv:1312.0719 by R. Blumenhagen, MF, F. Haßler, D.
More informationNonlinear MHD Stability and Dynamical Accessibility
Nonlinear MHD Stability and Dynamical Accessibility Jean-Luc Thiffeault Department of Applied Physics and Applied Mathematics Columbia University Philip J. Morrison Department of Physics and Institute
More informationSpace Physics. An Introduction to Plasmas and Particles in the Heliosphere and Magnetospheres. May-Britt Kallenrode. Springer
May-Britt Kallenrode Space Physics An Introduction to Plasmas and Particles in the Heliosphere and Magnetospheres With 170 Figures, 9 Tables, Numerous Exercises and Problems Springer Contents 1. Introduction
More informationEffects of spin-orbit coupling on the BKT transition and the vortexantivortex structure in 2D Fermi Gases
Effects of spin-orbit coupling on the BKT transition and the vortexantivortex structure in D Fermi Gases Carlos A. R. Sa de Melo Georgia Institute of Technology QMath13 Mathematical Results in Quantum
More informationA Brief Introduction to AdS/CFT Correspondence
Department of Physics Universidad de los Andes Bogota, Colombia 2011 Outline of the Talk Outline of the Talk Introduction Outline of the Talk Introduction Motivation Outline of the Talk Introduction Motivation
More informationIf I only had a Brane
If I only had a Brane A Story about Gravity and QCD. on 20 slides and in 40 minutes. AdS/CFT correspondence = Anti de Sitter / Conformal field theory correspondence. Chapter 1: String Theory in a nutshell.
More informationPoisson Manifolds Bihamiltonian Manifolds Bihamiltonian systems as Integrable systems Bihamiltonian structure as tool to find solutions
The Bi hamiltonian Approach to Integrable Systems Paolo Casati Szeged 27 November 2014 1 Poisson Manifolds 2 Bihamiltonian Manifolds 3 Bihamiltonian systems as Integrable systems 4 Bihamiltonian structure
More informationSymmetric Surfaces of Topological Superconductor
Symmetric Surfaces of Topological Superconductor Sharmistha Sahoo Zhao Zhang Jeffrey Teo Outline Introduction Brief description of time reversal symmetric topological superconductor. Coupled wire model
More informationTopological Physics in Band Insulators IV
Topological Physics in Band Insulators IV Gene Mele University of Pennsylvania Wannier representation and band projectors Modern view: Gapped electronic states are equivalent Kohn (1964): insulator is
More informationHolographic renormalization and reconstruction of space-time. Kostas Skenderis Southampton Theory Astrophysics and Gravity research centre
Holographic renormalization and reconstruction of space-time Southampton Theory Astrophysics and Gravity research centre STAG CH RESEARCH ER C TE CENTER Holographic Renormalization and Entanglement Paris,
More informationPhysical Dynamics (SPA5304) Lecture Plan 2018
Physical Dynamics (SPA5304) Lecture Plan 2018 The numbers on the left margin are approximate lecture numbers. Items in gray are not covered this year 1 Advanced Review of Newtonian Mechanics 1.1 One Particle
More informationConfinement of toroidal non-neutral plasma in Proto-RT
Workshop on Physics with Ultra Slow Antiproton Beams, RIKEN, March 15, 2005 Confinement of toroidal non-neutral plasma in Proto-RT H. Saitoh, Z. Yoshida, and S. Watanabe Graduate School of Frontier Sciences,
More informationOn the Hamilton-Jacobi Variational Formulation of the Vlasov Equation
On the Hamilton-Jacobi Variational Formulation of the Vlasov Equation P. J. Morrison epartment of Physics and Institute for Fusion Studies, University of Texas, Austin, Texas 7871-1060, USA. (ated: January
More informationTopological Insulators in 3D and Bosonization
Topological Insulators in 3D and Bosonization Andrea Cappelli, INFN Florence (w. E. Randellini, J. Sisti) Outline Topological states of matter: bulk and edge Fermions and bosons on the (1+1)-dimensional
More informationBlack Holes, Integrable Systems and Soft Hair
Ricardo Troncoso Black Holes, Integrable Systems and Soft Hair based on arxiv: 1605.04490 [hep-th] In collaboration with : A. Pérez and D. Tempo Centro de Estudios Científicos (CECs) Valdivia, Chile Introduction
More informationELECTROHYDRODYNAMICS IN DUSTY AND DIRTY PLASMAS
ELECTROHYDRODYNAMICS IN DUSTY AND DIRTY PLASMAS Gravito-Electrodynamics and EHD by HIROSHI KIKUCHI Institute for Environmental Electromagnetics, Tokyo, Japan KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON
More informationConfinement of toroidal non-neutral plasma in Proto-RT
Workshop on Physics with Ultra Slow Antiproton Beams, RIKEN, March 15, 2005 Confinement of toroidal non-neutral plasma in Proto-RT H. Saitoh, Z. Yoshida, and S. Watanabe Graduate School of Frontier Sciences,
More informationTheory for Neoclassical Toroidal Plasma Viscosity in a Toroidally Symmetric Torus. K. C. Shaing
Theory for Neoclassical Toroidal Plasma Viscosity in a Toroidally Symmetric Torus K. C. Shaing Plasma and Space Science Center, and ISAPS, National Cheng Kung University, Tainan, Taiwan 70101, Republic
More informationHigh performance computing and numerical modeling
High performance computing and numerical modeling Volker Springel Plan for my lectures Lecture 1: Collisional and collisionless N-body dynamics Lecture 2: Gravitational force calculation Lecture 3: Basic
More informationChris Verhaaren Joint Theory Seminar 31 October With Zackaria Chacko, Rashmish Mishra, and Simon Riquelme
Chris Verhaaren Joint Theory Seminar 31 October 2016 With Zackaria Chacko, Rashmish Mishra, and Simon Riquelme It s Halloween A time for exhibiting what some find frightening And seeing that it s not so
More informationGauge Fixing and Constrained Dynamics in Numerical Relativity
Gauge Fixing and Constrained Dynamics in Numerical Relativity Jon Allen The Dirac formalism for dealing with constraints in a canonical Hamiltonian formulation is reviewed. Gauge freedom is discussed and
More informationIV. Classical Statistical Mechanics
IV. Classical Statistical Mechanics IV.A General Definitions Statistical Mechanics is a probabilistic approach to equilibrium macroscopic properties of large numbers of degrees of freedom. As discussed
More informationPhysics 106b: Lecture 7 25 January, 2018
Physics 106b: Lecture 7 25 January, 2018 Hamiltonian Chaos: Introduction Integrable Systems We start with systems that do not exhibit chaos, but instead have simple periodic motion (like the SHO) with
More informationWiggling Throat of Extremal Black Holes
Wiggling Throat of Extremal Black Holes Ali Seraj School of Physics Institute for Research in Fundamental Sciences (IPM), Tehran, Iran Recent Trends in String Theory and Related Topics May 2016, IPM based
More informationTopics for the Qualifying Examination
Topics for the Qualifying Examination Quantum Mechanics I and II 1. Quantum kinematics and dynamics 1.1 Postulates of Quantum Mechanics. 1.2 Configuration space vs. Hilbert space, wave function vs. state
More informationCurves in the configuration space Q or in the velocity phase space Ω satisfying the Euler-Lagrange (EL) equations,
Physics 6010, Fall 2010 Hamiltonian Formalism: Hamilton s equations. Conservation laws. Reduction. Poisson Brackets. Relevant Sections in Text: 8.1 8.3, 9.5 The Hamiltonian Formalism We now return to formal
More informationSupersymmetric Gauge Theories in 3d
Supersymmetric Gauge Theories in 3d Nathan Seiberg IAS Intriligator and NS, arxiv:1305.1633 Aharony, Razamat, NS, and Willett, arxiv:1305.3924 3d SUSY Gauge Theories New lessons about dynamics of quantum
More informationFINAL EXAM GROUND RULES
PHYSICS 507 Fall 2011 FINAL EXAM Room: ARC-108 Time: Wednesday, December 21, 10am-1pm GROUND RULES There are four problems based on the above-listed material. Closed book Closed notes Partial credit will
More informationPhysical Dynamics (PHY-304)
Physical Dynamics (PHY-304) Gabriele Travaglini March 31, 2012 1 Review of Newtonian Mechanics 1.1 One particle Lectures 1-2. Frame, velocity, acceleration, number of degrees of freedom, generalised coordinates.
More informationFirst-Principles Calculation of Topological Invariants (Wannier Functions Approach) Alexey A. Soluyanov
First-Principles Calculation of Topological Invariants (Wannier Functions Approach) Alexey A. Soluyanov ES'12, WFU, June 8, 212 The present work was done in collaboration with David Vanderbilt Outline:
More informationHamiltonian Dynamics
Hamiltonian Dynamics CDS 140b Joris Vankerschaver jv@caltech.edu CDS Feb. 10, 2009 Joris Vankerschaver (CDS) Hamiltonian Dynamics Feb. 10, 2009 1 / 31 Outline 1. Introductory concepts; 2. Poisson brackets;
More informationReview for Final. elementary mechanics. Lagrangian and Hamiltonian Dynamics. oscillations
Review for Final elementary mechanics Newtonian mechanics gravitation dynamics of systems of particles Lagrangian and Hamiltonian Dynamics Lagrangian mechanics Variational dynamics Hamiltonian dynamics
More information2 Canonical quantization
Phys540.nb 7 Canonical quantization.1. Lagrangian mechanics and canonical quantization Q: How do we quantize a general system?.1.1.lagrangian Lagrangian mechanics is a reformulation of classical mechanics.
More informationGeneralized Global Symmetries
Generalized Global Symmetries Anton Kapustin Simons Center for Geometry and Physics, Stony Brook April 9, 2015 Anton Kapustin (Simons Center for Geometry and Physics, Generalized StonyGlobal Brook) Symmetries
More informationOverview of Gyrokinetic Theory & Properties of ITG/TEM Instabilities
Overview of Gyrokinetic Theory & Properties of ITG/TEM Instabilities G. W. Hammett Princeton Plasma Physics Lab (PPPL) http://w3.pppl.gov/~hammett AST559: Plasma & Fluid Turbulence Dec. 5, 2011 (based
More informationII. Spontaneous symmetry breaking
. Spontaneous symmetry breaking .1 Weinberg s chair Hamiltonian rotational invariant eigenstates of good angular momentum: M > have a density distribution that is an average over all orientations with
More informationLecture 3: The Navier-Stokes Equations: Topological aspects
Lecture 3: The Navier-Stokes Equations: Topological aspects September 9, 2015 1 Goal Topology is the branch of math wich studies shape-changing objects; objects which can transform one into another without
More informationEtienne Forest. From Tracking Code. to Analysis. Generalised Courant-Snyder Theory for Any Accelerator Model. 4 } Springer
Etienne Forest From Tracking Code to Analysis Generalised Courant-Snyder Theory for Any Accelerator Model 4 } Springer Contents 1 Introduction 1 1.1 Dichotomous Approach Derived from Complexity 1 1.2 The
More informationSymmetries, Conservation Laws and Hamiltonian Structures in Geophysical Fluid Dynamics
Symmetries, Conservation Laws and Hamiltonian Structures in Geophysical Fluid Dynamics Miguel A. Jiménez-Urias 1 Department of Oceanography University of Washington AMATH 573 1 Kinematics Canonical vs
More informationCausal nature and dynamics of trapping horizon in black hole collapse
Causal nature and dynamics of trapping horizon in black hole collapse Ilia Musco (CNRS, Observatoire de Paris/Meudon - LUTH) KSM 2017- FIAS (Frankfurt) 24-28 July 2017 Classical and Quantum Gravity Vol.
More informationThe Dirac composite fermions in fractional quantum Hall effect. Dam Thanh Son (University of Chicago) Nambu Memorial Symposium March 12, 2016
The Dirac composite fermions in fractional quantum Hall effect Dam Thanh Son (University of Chicago) Nambu Memorial Symposium March 12, 2016 A story of a symmetry lost and recovered Dam Thanh Son (University
More informationOutline for Fundamentals of Statistical Physics Leo P. Kadanoff
Outline for Fundamentals of Statistical Physics Leo P. Kadanoff text: Statistical Physics, Statics, Dynamics, Renormalization Leo Kadanoff I also referred often to Wikipedia and found it accurate and helpful.
More informationHamiltonian Dynamics from Lie Poisson Brackets
1 Hamiltonian Dynamics from Lie Poisson Brackets Jean-Luc Thiffeault Department of Applied Physics and Applied Mathematics Columbia University http://plasma.ap.columbia.edu/~jeanluc 12 February 2002 2
More informationLIE ALGEBROIDS AND POISSON GEOMETRY, OLIVETTI SEMINAR NOTES
LIE ALGEBROIDS AND POISSON GEOMETRY, OLIVETTI SEMINAR NOTES BENJAMIN HOFFMAN 1. Outline Lie algebroids are the infinitesimal counterpart of Lie groupoids, which generalize how we can talk about symmetries
More informationDeconfined Quantum Critical Points
Deconfined Quantum Critical Points Leon Balents T. Senthil, MIT A. Vishwanath, UCB S. Sachdev, Yale M.P.A. Fisher, UCSB Outline Introduction: what is a DQCP Disordered and VBS ground states and gauge theory
More informationCriticality in topologically ordered systems: a case study
Criticality in topologically ordered systems: a case study Fiona Burnell Schulz & FJB 16 FJB 17? Phases and phase transitions ~ 194 s: Landau theory (Liquids vs crystals; magnets; etc.) Local order parameter
More informationIntroduction to Particle Physics
Introduction to Particle Physics The Particle Zoo Symmetries The Standard Model Thomas Gajdosik Vilnius Universitetas Teorinės Fizikos Katedra Introduction to Particle Physics http://web.vu.lt/ff/t.gajdosik/wop/
More informationFormation of High-b ECH Plasma and Inward Particle Diffusion in RT-1
J Fusion Energ (2010) 29:553 557 DOI 10.1007/s10894-010-9327-6 ORIGINAL RESEARCH Formation of High-b ECH Plasma and Inward Particle Diffusion in RT-1 H. Saitoh Z. Yoshida J. Morikawa Y. Yano T. Mizushima
More informationIs the composite fermion a Dirac particle?
Is the composite fermion a Dirac particle? Dam T. Son (University of Chicago) Cold atoms meet QFT, 2015 Ref.: 1502.03446 Plan Plan Composite fermion: quasiparticle of Fractional Quantum Hall Effect (FQHE)
More informationLecture Note 1. 99% of the matter in the universe is in the plasma state. Solid -> liquid -> Gas -> Plasma (The fourth state of matter)
Lecture Note 1 1.1 Plasma 99% of the matter in the universe is in the plasma state. Solid -> liquid -> Gas -> Plasma (The fourth state of matter) Recall: Concept of Temperature A gas in thermal equilibrium
More informationEmergent topological phenomena in antiferromagnets with noncoplanar spins
Emergent topological phenomena in antiferromagnets with noncoplanar spins - Surface quantum Hall effect - Dimensional crossover Bohm-Jung Yang (RIKEN, Center for Emergent Matter Science (CEMS), Japan)
More informationFundamentals of Plasma Physics Basic concepts
Fundamentals of Plasma Physics Basic concepts APPLAuSE Instituto Superior Técnico Instituto de Plasmas e Fusão Nuclear Vasco Guerra Since the dawn of Mankind men has tried to understand plasma physics...
More informationThe Big Picture. Thomas Schaefer. North Carolina State University
The Big Picture Thomas Schaefer North Carolina State University 1 Big Questions What is QCD? What is a Phase of QCD? What is a Plasma? What is a (perfect) Liquid? What is a wqgp/sqgp? 2 What is QCD (Quantum
More informationList of Comprehensive Exams Topics
List of Comprehensive Exams Topics Mechanics 1. Basic Mechanics Newton s laws and conservation laws, the virial theorem 2. The Lagrangian and Hamiltonian Formalism The Lagrange formalism and the principle
More informationThe Langlands dual group and Electric-Magnetic Duality
The Langlands dual group and Electric-Magnetic Duality DESY (Theory) & U. Hamburg (Dept. of Math) Nov 10, 2015 DESY Fellows Meeting Outline My hope is to answer the question : Why should physicists pay
More informationTopological Phases in One Dimension
Topological Phases in One Dimension Lukasz Fidkowski and Alexei Kitaev arxiv:1008.4138 Topological phases in 2 dimensions: - Integer quantum Hall effect - quantized σ xy - robust chiral edge modes - Fractional
More informationFinite Ring Geometries and Role of Coupling in Molecular Dynamics and Chemistry
Finite Ring Geometries and Role of Coupling in Molecular Dynamics and Chemistry Petr Pracna J. Heyrovský Institute of Physical Chemistry Academy of Sciences of the Czech Republic, Prague ZiF Cooperation
More informationVortex States in a Non-Abelian Magnetic Field
Vortex States in a Non-Abelian Magnetic Field Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University SESAPS November 10, 2016 Acknowledgments Collin Broholm IQM
More informationTop-down Causality the missing link in our physical theories
Top-down Causality the missing link in our physical theories Jose P Koshy josepkoshy@gmail.com Abstract: Confining is a top-down effect. Particles have to be confined in a region if these are to bond together.
More informationEMERGENT GRAVITY AND COSMOLOGY: THERMODYNAMIC PERSPECTIVE
EMERGENT GRAVITY AND COSMOLOGY: THERMODYNAMIC PERSPECTIVE Master Colloquium Pranjal Dhole University of Bonn Supervisors: Prof. Dr. Claus Kiefer Prof. Dr. Pavel Kroupa May 22, 2015 Work done at: Institute
More informationThe Physics of Fluids and Plasmas
The Physics of Fluids and Plasmas An Introduction for Astrophysicists ARNAB RAI CHOUDHURI CAMBRIDGE UNIVERSITY PRESS Preface Acknowledgements xiii xvii Introduction 1 1. 3 1.1 Fluids and plasmas in the
More informationCharge of the Electron, and the Constants of Radiation According to J. A. Wheeler s Geometrodynamic Model
Volume 4 PROGRESS IN PHYSICS October, 200 Charge of the Electron, and the Constants of Radiation According to J. A. Wheeler s Geometrodynamic Model Anatoly V. Belyakov E-mail: belyakov.lih@gmail.com This
More informationDirac structures. Henrique Bursztyn, IMPA. Geometry, mechanics and dynamics: the legacy of J. Marsden Fields Institute, July 2012
Dirac structures Henrique Bursztyn, IMPA Geometry, mechanics and dynamics: the legacy of J. Marsden Fields Institute, July 2012 Outline: 1. Mechanics and constraints (Dirac s theory) 2. Degenerate symplectic
More informationSingle Particle Motion in a Magnetized Plasma
Single Particle Motion in a Magnetized Plasma Aurora observed from the Space Shuttle Bounce Motion At Earth, pitch angles are defined by the velocity direction of particles at the magnetic equator, therefore:
More informationS-CONFINING DUALITIES
DIMENSIONAL REDUCTION of S-CONFINING DUALITIES Cornell University work in progress, in collaboration with C. Csaki, Y. Shirman, F. Tanedo and J. Terning. 1 46 3D Yang-Mills A. M. Polyakov, Quark Confinement
More informationUniversal phase transitions in Topological lattice models
Universal phase transitions in Topological lattice models F. J. Burnell Collaborators: J. Slingerland S. H. Simon September 2, 2010 Overview Matter: classified by orders Symmetry Breaking (Ferromagnet)
More informationPhysical Processes in Astrophysics
Physical Processes in Astrophysics Huirong Yan Uni Potsdam & Desy Email: hyan@mail.desy.de 1 Reference Books: Plasma Physics for Astrophysics, Russell M. Kulsrud (2005) The Physics of Astrophysics, Frank
More informationNovember 24, Energy Extraction from Black Holes. T. Daniel Brennan. Special Relativity. General Relativity. Black Holes.
from November 24, 2014 1 2 3 4 5 Problem with Electricity and Magnetism In the late 1800 s physicists realized there was a problem with electromagnetism: the speed of light was given in terms of fundamental
More informationSymplectic and Poisson Manifolds
Symplectic and Poisson Manifolds Harry Smith In this survey we look at the basic definitions relating to symplectic manifolds and Poisson manifolds and consider different examples of these. We go on to
More informationBuckingham s magical pi theorem
Buckingham s magical pi theorem and the Lie symmetries of nature Harald Hanche-Olsen Theoretical physics colloquium 2002 11 05 p.1/31 A simple example θ λ The period t depends on λ, g, θ max. But how?
More informationVortices and vortex states of Rashba spin-orbit coupled condensates
Vortices and vortex states of Rashba spin-orbit coupled condensates Predrag Nikolić George Mason University Institute for Quantum Matter @ Johns Hopkins University March 5, 2014 P.N, T.Duric, Z.Tesanovic,
More informationSingle particle motion and trapped particles
Single particle motion and trapped particles Gyromotion of ions and electrons Drifts in electric fields Inhomogeneous magnetic fields Magnetic and general drift motions Trapped magnetospheric particles
More informationOutline. 1 Geometry and Commutative Algebra. 2 Singularities and Resolutions. 3 Noncommutative Algebra and Deformations. 4 Representation Theory
Outline Geometry, noncommutative algebra and representations Iain Gordon http://www.maths.ed.ac.uk/ igordon/ University of Edinburgh 16th December 2006 1 2 3 4 1 Iain Gordon Geometry, noncommutative algebra
More informationStellar Evolution: Outline
Stellar Evolution: Outline Interstellar Medium (dust) Hydrogen and Helium Small amounts of Carbon Dioxide (makes it easier to detect) Massive amounts of material between 100,000 and 10,000,000 solar masses
More informationFundamental Physics at ACT. Sante Carloni, ACT
Fundamental Physics at ACT Sante Carloni, ACT Areas of Interest Research in Fundamental Physics is focused on the impact that new ideas in physics can have on the space sector. ACT Fundamental Physics
More information5 Topological defects and textures in ordered media
5 Topological defects and textures in ordered media In this chapter we consider how to classify topological defects and textures in ordered media. We give here only a very short account of the method following
More informationSOME OBSERVATIONS REGARDING BRACKETS AND DISSIPATION. Philip J.Morrison of Mathematics University of California Berkeley, CA 94720
SOME OBSERVATIONS REGARDING BRACKETS AND DISSIPATION + Philip J.Morrison of Mathematics University of California Berkeley, CA 94720 D~partment Abstract Some ideas relating to a bracket formulation for
More informationSymmetries and Dynamics of Discrete Systems
Symmetries and Dynamics of Discrete Systems Talk at CASC 2007, Bonn, Germany Vladimir Kornyak Laboratory of Information Technologies Joint Institute for Nuclear Research 19 September 2007 V. V. Kornyak
More informationDuality and Holography
Duality and Holography? Joseph Polchinski UC Davis, 5/16/11 Which of these interactions doesn t belong? a) Electromagnetism b) Weak nuclear c) Strong nuclear d) a) Electromagnetism b) Weak nuclear c) Strong
More informationIntroduction. Chapter Plasma: definitions
Chapter 1 Introduction 1.1 Plasma: definitions A plasma is a quasi-neutral gas of charged and neutral particles which exhibits collective behaviour. An equivalent, alternative definition: A plasma is a
More informationClassification of Symmetry Protected Topological Phases in Interacting Systems
Classification of Symmetry Protected Topological Phases in Interacting Systems Zhengcheng Gu (PI) Collaborators: Prof. Xiao-Gang ang Wen (PI/ PI/MIT) Prof. M. Levin (U. of Chicago) Dr. Xie Chen(UC Berkeley)
More information1 Hamiltonian formalism
1 Hamiltonian formalism 1.1 Hamilton s principle of stationary action A dynamical system with a finite number n degrees of freedom can be described by real functions of time q i (t) (i =1, 2,..., n) which,
More informationField Theory Description of Topological States of Matter. Andrea Cappelli INFN, Florence (w. E. Randellini, J. Sisti)
Field Theory Description of Topological States of Matter Andrea Cappelli INFN, Florence (w. E. Randellini, J. Sisti) Topological States of Matter System with bulk gap but non-trivial at energies below
More information