Perfect Fluidity in Cold Atomic Gases?

Size: px
Start display at page:

Download "Perfect Fluidity in Cold Atomic Gases?"

Transcription

1 Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1

2 2

3 Hydrodynamics Long-wavelength, low-frequency dynamics of conserved or spontaneoulsy broken symmetry variables. τ τ micro τ λ 1 Historically: Water (ρ, ǫ, π) 3

4 Example: Simple Fluid Continuity equation ρ t + (ρ v) = 0 Euler (Navier-Stokes) equation t (ρv i) + Π ij = 0 x j Energy momentum tensor Π ij = Pδ ij + ρv i v j + η reactive ( i v j + j v i 23 δ ij k v k ) dissipative

5 Elliptic Flow Hydrodynamic expansion converts coordinate space anisotropy to momentum space anisotropy Anisotropy Parameter v Hydro model π K p Λ PHENIX Data π + +π K +K p+p STAR Data 0 K S Λ+Λ b Transverse Momentum p T (GeV/c) source: U. Heinz (2005) 5

6 Elliptic Flow II v 2 /ε 0.25 HYDRO limits E lab /A=11.8 GeV, E877 E lab /A=40 GeV, NA E lab /A=158 GeV, NA49 s NN =130 GeV, STAR s NN =200 GeV, STAR Prelim (1/S) dn ch /dy Requires perfect fluidity (η/s < 0.1?) (s)qgp saturates (conjectured) universal bound η/s = 1/(4π)? 6

7 Viscosity Bound: Rough Argument Kinetic theory estimate of shear viscosity η 1 3 n vml = 2 3 n ( 1 2 m v2 ) l v = 2 3 neτ mft Entropy density: s k B n. Uncertainty relation implies η s neτ mft k B n Eτ mft k B k B Validity of kinetic theory as Eτ? Why η/s? Why not η/n? 7

8 Holographic Duals at Finite Temperature Thermal (conformal) field theory AdS 5 black hole CFT temperature CFT entropy Strong coupling limit s = π2 2 N2 c T 3 = 3 4 s 0 Gubser and Klebanov Hawking temperature of black hole Hawking-Bekenstein entropy area of event horizon s weak coupling strong coupling λ = g 2 N Extended to transport properties by Policastro, Son and Starinets 8

9 Quark Gluon Plasma Equation of State (Lattice) 7 6 p/t ε/t 4 ε SB /T 4 15% n f =(2+1),N τ =4 N τ =6 n f =2, N τ =4 N τ =6 p SB /T p4, N τ =4, n f =3 asqtad, N τ =6, n f =2+1 0 T/T T/T c Compilation by F. Karsch (SciDAC) 9

10 Holographic Duals: Transport Properties Thermal (conformal) field theory AdS 5 black hole CFT entropy shear viscosity Strong coupling limit Hawking-Bekenstein entropy area of event horizon Graviton absorption cross section area of event horizon η s η s = 4πk B Son and Starinets h 4πk B Strong coupling limit universal? Provides lower bound for all theories? 0 g 2 N c 10

11 Viscosity Bound: Common Fluids 4π η h s Helium 0.1MPa Nitrogen 10MPa Water 100MPa Viscosity bound T, K 11

12 Viscosity Bound: Counter Examples? non relativistic systems: can make S/N large η s = 1 log(n s ) c mt a 2 n modified conjecture: applies to systems that can be embedded in a relativistic (gauge?) theory T. Cohen: Consider heavy-light mesons in QCD with N F = N c m Q = m 0 QN F n = η s 1 log(n s ) n 0 log(n F ), T = T 0 N F log(n F ) 1/2 stable fluid? s well defined? 12

13 Designer Fluids Atomic gas with two spin states: and V closed open r Feshbach resonance a(b) = a 0 ( 1 + B B 0 ) Unitarity limit a 13 σ = 4π k 2

14 Why are these systems interesting? System is intrinsically quantum mechanical cross section saturates unitarity bound System is scale invariant at unitarity. Universal thermodynamics E ( E ) A = ξ = ξ 3 ( k 2 F A 0 5 2M System is strongly coupled but dilute (k F a) (k F r) 0 ) Strong elliptic flow observed experimentally 14

15 Elliptic Flow Hydrodynamic expansion converts σ σ µ coordinate space anisotropy σ σ to momentum space anisotropy 15

16 Collective Modes Radial breathing mode Kinast et al. (2005) 2.00 B (Gauss) Frequency (ω/ω ) /k F a Ideal fluid hydrodynamics, equation of state P n 5/3 n t + (n v) = 0 v ( t + v ) v = 1 P mn 1 V m ω = 10 3 ω 16

17 Damping of Collective Excitations 60 (a) (<x 2 >) (1/2) ( µm) (b) (c) Damping rate (1/τω ) T ~ t hold (ms) 6 8 T/T F = (0.5,0.33,0.17) τω: decay time trap frequency Kinast et al. (2005) 17

18 Viscous Hydrodynamics Energy dissipation (η, ζ, κ: shear, bulk viscosity, heat conductivity) Ė = η d 3 x ( i v j + j v i 23 ) 2 2 δ ij k v k ζ d 3 x ( i v i ) 2 κ d 3 x ( i T) 2 T Shear viscosity to entropy ratio (assuming ζ =κ=0) η/s η s = 3 4 ξ 1 2 (3N) 1 3 Γ ω ω N ω S see also Bruun, Smith, Gelman et T/T F al. 18

19 Damping dominated by shear viscosity? Study dependence on flow pattern Study particle number scaling viscous hydro: Γ N 1/3 Boltzmann: Γ N 1/3 Role of thermal conductivity? suppressed for scaling flows: δt T(δn/n) const 19

20 Kinetic Theory Quasi-Particles: Kinetic Theory T ij = d 3 p p ip j E p f p, Boltzmann equation f p t + v x f p + F p f p = C[f p ] Linearized theory (Chapman-Enskog): f p = f 0 p(1 + χ p /T) η χ X 2 χ C χ χ X = d 3 p f 0 p χ p p ij v ij v ij = v 2 δ ij 3v i v j 20

21 Low T: Phonons High T: Atoms Η s T T F η ( T ) 1 ) 3/2 log ( T ( TF ) 8 η + + s T s T F T F 21

22 Free scaling expansion n(r, r z ) = 1 b 2 b z b = Viscous damping n 0 ( r b, r z b z ) ω 2 Elliptic Flow R i /R 0 z b (b 2 b z) γ Ė = 4 E/(µN) (ḃ ḃz ) 2 d x η(x) b b z E kin E int E(3 KSS) E = 0.05 E(KSS) dt Ė converges quickly R R z ω t ω t 22

23 Elliptic Flow (cont) Can define v 2 = cos(2φ) as in HI collisions 1 v ǫ = ǫ = 2z2 x 2 + y 2 z 2 + x 2 + y v/v max Can also sweep to BEC regime and simulate recombination models 23

24 Final Thoughts Cold atomic gases provide interesting, strongly coupled, model system in which to study sources of dissipation. η/s 1/2 Smaller than any other known liquid (except for QGP?). Since other sources of dissipation exist, this is really an upper bound. There are reliable calculations of η/s at high T (Bruun, Smith,...) and low T (Rupak and T.S). Extrapolate to T T F 24

25 Conjectured bound has a smooth non-relativistic limit. Note that the a limit can also be realized in QCD (by tuning µ, µ e and m q ). But: In non-relativistic systems s n possible Purely field theoretic proofs? N = 4 SUSY YM is special because there is no phase transition. In real systems there is a phase transition as the coupling becomes large, and the new phase (confined in QCD, superfluid in the atomic system) has weakly coupled low energy excitations, and a large viscosity. No quasi-particles in sqgp? 25

Perfect Fluidity in Cold Atomic Gases?

Perfect Fluidity in Cold Atomic Gases? Perfect Fluidity in Cold Atomic Gases? Thomas Schaefer North Carolina State University 1 Hydrodynamics Long-wavelength, low-frequency dynamics of conserved or spontaneoulsy broken symmetry variables τ

More information

Perfect Fluidity in Cold Atomic Gases?

Perfect 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 information

Perfect Fluids: From Nano to Tera

Perfect 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 Long-wavelength,

More information

UN PICCOLO BIG BANG IN LABORATORIO: L'ESPERIMENTO ALICE AD LHC

UN PICCOLO BIG BANG IN LABORATORIO: L'ESPERIMENTO ALICE AD LHC UN PICCOLO BIG BANG IN LABORATORIO: L'ESPERIMENTO ALICE AD LHC Parte 1: Carlos A. Salgado Universidade de Santiago de Compostela csalgado@usc.es http://cern.ch/csalgado LHC physics program Fundamental

More information

The effects of angular momentum conservation in relativistic heavy ion collisions

The effects of angular momentum conservation in relativistic heavy ion collisions conservation in relativistic heavy ion collisions Università di Firenze and INFN Sezione di Firenze, Firenze, Italy E-mail: author@email F. Piccinini INFN Sezione di Pavia, Pavia, Italy E-mail: piccinini@pv.infn.it

More information

FLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions

FLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or

More information

Vacuum Technology. Kinetic Theory of Gas. Dr. Philip D. Rack

Vacuum Technology. Kinetic Theory of Gas. Dr. Philip D. Rack Kinetic Theory of Gas Assistant Professor Department of Materials Science and Engineering University of Tennessee 603 Dougherty Engineering Building Knoxville, TN 3793-00 Phone: (865) 974-5344 Fax (865)

More information

Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows

Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows Lecture 3 Fluid Dynamics and Balance Equa6ons for Reac6ng Flows 3.- 1 Basics: equations of continuum mechanics - balance equations for mass and momentum - balance equations for the energy and the chemical

More information

University of Maryland Fraternity & Sorority Life Spring 2015 Academic Report

University of Maryland Fraternity & Sorority Life Spring 2015 Academic Report University of Maryland Fraternity & Sorority Life Academic Report Academic and Population Statistics Population: # of Students: # of New Members: Avg. Size: Avg. GPA: % of the Undergraduate Population

More information

Basic Principles in Microfluidics

Basic Principles in Microfluidics Basic Principles in Microfluidics 1 Newton s Second Law for Fluidics Newton s 2 nd Law (F= ma) : Time rate of change of momentum of a system equal to net force acting on system!f = dp dt Sum of forces

More information

What is Energy conservation Rate in the Universe?

What is Energy conservation Rate in the Universe? Thermal Equilibrium Energy conservation equation Heating by photoionization Cooling by recombination Cooling by brehmsstralung Cooling by collisionally excited lines Collisional de-excitation Detailed

More information

Statistical Physics, Part 2 by E. M. Lifshitz and L. P. Pitaevskii (volume 9 of Landau and Lifshitz, Course of Theoretical Physics).

Statistical 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 non-interacting. This free electron model describes the electrons in the outermost shell of the

More information

Nara Women s University, Nara, Japan B.A. Honors in physics 2002 March 31 Thesis: Particle Production in Relativistic Heavy Ion Collisions

Nara Women s University, Nara, Japan B.A. Honors in physics 2002 March 31 Thesis: Particle Production in Relativistic Heavy Ion Collisions Maya SHIMOMURA Brookhaven National Laboratory, Upton, NY, 11973, U.S.A. PROFILE I am an experimentalist working for high-energy heavy ion at Iowa State University as a postdoctoral research associate.

More information

11 Navier-Stokes equations and turbulence

11 Navier-Stokes equations and turbulence 11 Navier-Stokes equations and turbulence So far, we have considered ideal gas dynamics governed by the Euler equations, where internal friction in the gas is assumed to be absent. Real fluids have internal

More information

Basic Equations, Boundary Conditions and Dimensionless Parameters

Basic Equations, Boundary Conditions and Dimensionless Parameters Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were

More information

Topic 3b: Kinetic Theory

Topic 3b: Kinetic Theory Topic 3b: Kinetic Theory What is temperature? We have developed some statistical language to simplify describing measurements on physical systems. When we measure the temperature of a system, what underlying

More information

Free Electron Fermi Gas (Kittel Ch. 6)

Free Electron Fermi Gas (Kittel Ch. 6) Free Electron Fermi Gas (Kittel Ch. 6) Role of Electrons in Solids Electrons are responsible for binding of crystals -- they are the glue that hold the nuclei together Types of binding (see next slide)

More information

Masses in Atomic Units

Masses in Atomic Units Nuclear Composition - the forces binding protons and neutrons in the nucleus are much stronger (binding energy of MeV) than the forces binding electrons to the atom (binding energy of ev) - the constituents

More information

1 The basic equations of fluid dynamics

1 The basic equations of fluid dynamics 1 The basic equations of fluid dynamics The main task in fluid dynamics is to find the velocity field describing the flow in a given domain. To do this, one uses the basic equations of fluid flow, which

More information

Neutron stars as laboratories for exotic physics

Neutron 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 information

arxiv:1507.00499v1 [nucl-th] 2 Jul 2015

arxiv:1507.00499v1 [nucl-th] 2 Jul 2015 Flow anisotropies due to momentum deposition from hard partons Boris Tomášik a,b, Martin Schulc b,c arxiv:1507.00499v1 [nucl-th] 2 Jul 2015 a Univerzita Mateja Bela, Banská Bystrica, Slovakia b FNSPE,

More information

Parabolic Equations. Chapter 5. Contents. 5.1.2 Well-Posed Initial-Boundary Value Problem. 5.1.3 Time Irreversibility of the Heat Equation

Parabolic Equations. Chapter 5. Contents. 5.1.2 Well-Posed Initial-Boundary Value Problem. 5.1.3 Time Irreversibility of the Heat Equation 7 5.1 Definitions Properties Chapter 5 Parabolic Equations Note that we require the solution u(, t bounded in R n for all t. In particular we assume that the boundedness of the smooth function u at infinity

More information

Spontaneous symmetry breaking in particle physics: a case of cross fertilization

Spontaneous 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 Jona-Lasinio Nobel Lecture December 8, 2008 1 / 25 History repeats itself 1960

More information

Lecture 24 - Surface tension, viscous flow, thermodynamics

Lecture 24 - Surface tension, viscous flow, thermodynamics Lecture 24 - Surface tension, viscous flow, thermodynamics Surface tension, surface energy The atoms at the surface of a solid or liquid are not happy. Their bonding is less ideal than the bonding of atoms

More information

F en = mω 0 2 x. We should regard this as a model of the response of an atom, rather than a classical model of the atom itself.

F en = mω 0 2 x. We should regard this as a model of the response of an atom, rather than a classical model of the atom itself. The Electron Oscillator/Lorentz Atom Consider a simple model of a classical atom, in which the electron is harmonically bound to the nucleus n x e F en = mω 0 2 x origin resonance frequency Note: We should

More information

Compressible Fluids. Faith A. Morrison Associate Professor of Chemical Engineering Michigan Technological University November 4, 2004

Compressible Fluids. Faith A. Morrison Associate Professor of Chemical Engineering Michigan Technological University November 4, 2004 94 c 2004 Faith A. Morrison, all rights reserved. Compressible Fluids Faith A. Morrison Associate Professor of Chemical Engineering Michigan Technological University November 4, 2004 Chemical engineering

More information

Concepts in Theoretical Physics

Concepts 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 information

Energy Transport. Focus on heat transfer. Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids)

Energy Transport. Focus on heat transfer. Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids) Energy Transport Focus on heat transfer Heat Transfer Mechanisms: Conduction Radiation Convection (mass movement of fluids) Conduction Conduction heat transfer occurs only when there is physical contact

More information

Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid

Perpetual motion and driven dynamics of a mobile impurity in a quantum fluid and driven dynamics of a mobile impurity in a quantum fluid Oleg Lychkovskiy Russian Quantum Center Seminaire du LPTMS, 01.12.2015 Seminaire du LPTMS, 01.12.2015 1 / Plan of the talk 1 Perpetual motion

More information

Fundamentals of Statistical Physics Leo P. Kadanoff University of Chicago, USA

Fundamentals of Statistical Physics Leo P. Kadanoff University of Chicago, USA Fundamentals of Statistical Physics Leo P. Kadanoff University of Chicago, USA text: Statistical Physics, Statics, Dynamics, Renormalization Leo Kadanoff I also referred often to Wikipedia and found it

More information

Resistivity. V A = R = L ρ (1)

Resistivity. V A = R = L ρ (1) Resistivity Electric resistance R of a conductor depends on its size and shape as well as on the conducting material. The size- and shape-dependence was discovered by Georg Simon Ohm and is often treated

More information

Electromagnetic scattering of vector mesons in the Sakai-Sugimoto model.

Electromagnetic scattering of vector mesons in the Sakai-Sugimoto model. Electromagnetic scattering of vector mesons in the Sakai-Sugimoto model Carlos Alfonso Ballon Bayona, Durham University In collaboration with H. Boschi-Filho, N. R. F. Braga, M. Ihl and M. Torres. arxiv:0911.0023,

More information

3. Derive the partition function for the ideal monoatomic gas. Use Boltzmann statistics, and a quantum mechanical model for the gas.

3. 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 9.00-15.00. Lärare: Ingemar Bengtsson. Hjälpmedel: Penna, suddgummi och linjal. Bedömning: 3 poäng/uppgift. Betyg: 0-3 = F, 4-6

More information

Theoretical Particle Physics FYTN04: Oral Exam Questions, version ht15

Theoretical 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 information

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

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

More information

RANDOM INTERVAL HOMEOMORPHISMS. MICHA L MISIUREWICZ Indiana University Purdue University Indianapolis

RANDOM INTERVAL HOMEOMORPHISMS. MICHA L MISIUREWICZ Indiana University Purdue University Indianapolis RANDOM INTERVAL HOMEOMORPHISMS MICHA L MISIUREWICZ Indiana University Purdue University Indianapolis This is a joint work with Lluís Alsedà Motivation: A talk by Yulij Ilyashenko. Two interval maps, applied

More information

Instability, 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 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 information

Physics 176 Topics to Review For the Final Exam

Physics 176 Topics to Review For the Final Exam Physics 176 Topics to Review For the Final Exam Professor Henry Greenside May, 011 Thermodynamic Concepts and Facts 1. Practical criteria for identifying when a macroscopic system is in thermodynamic equilibrium:

More information

Lecture 8 - Turbulence. Applied Computational Fluid Dynamics

Lecture 8 - Turbulence. Applied Computational Fluid Dynamics Lecture 8 - Turbulence Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Turbulence What is turbulence? Effect of turbulence

More information

2. Illustration of the Nikkei 225 option data

2. Illustration of the Nikkei 225 option data 1. Introduction 2. Illustration of the Nikkei 225 option data 2.1 A brief outline of the Nikkei 225 options market τ 2.2 Estimation of the theoretical price τ = + ε ε = = + ε + = + + + = + ε + ε + ε =

More information

THERMAL TO ELECTRIC ENERGY CONVERSION

THERMAL TO ELECTRIC ENERGY CONVERSION THERMAL TO ELECTRIC ENERGY CONVERSION PETER L. HAGELSTEIN Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139,USA E-mail: plh@mit.edu As research in the area

More information

Basic Concepts in Nuclear Physics

Basic 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

Temperature anisotropy in the solar wind

Temperature anisotropy in the solar wind Introduction Observations Simulations Summary in the solar wind Petr Hellinger Institute of Atmospheric Physics & Astronomical Institute AS CR, Prague, Czech Republic Kinetic Instabilities, Plasma Turbulence

More information

1. Degenerate Pressure

1. Degenerate Pressure . Degenerate Pressure We next consider a Fermion gas in quite a different context: the interior of a white dwarf star. Like other stars, white dwarfs have fully ionized plasma interiors. The positively

More information

Nuclear Magnetic Resonance (NMR) Spectroscopy

Nuclear Magnetic Resonance (NMR) Spectroscopy April 28, 2016 Exam #3: Graded exams on Tuesday! Final Exam Tuesday, May 10 th, 10:30 a.m. Room: Votey 207 (tentative) Review Session: Sunday, May 8 th, 4 pm, Kalkin 325 (tentative) Office Hours Next week:

More information

FIELD THEORY OF ISING PERCOLATING CLUSTERS

FIELD THEORY OF ISING PERCOLATING CLUSTERS UK Meeting on Integrable Models and Conformal Field heory University of Kent, Canterbury 16-17 April 21 FIELD HEORY OF ISING PERCOLAING CLUSERS Gesualdo Delfino SISSA-rieste Based on : GD, Nucl.Phys.B

More information

Modeling and Simulations of Cavitating and Bubbly Flows

Modeling and Simulations of Cavitating and Bubbly Flows Muon Collider/Neutrino Factory Collaboration Meeting Riverside, California, January 27-31, 2004 Modeling and Simulations of Cavitating and Bubbly Flows Roman Samulyak Tianshi Lu, Yarema Prykarpatskyy Center

More information

Massless Black Holes & Black Rings as Effective Geometries of the D1-D5 System

Massless Black Holes & Black Rings as Effective Geometries of the D1-D5 System Massless Black Holes & Black Rings as Effective Geometries of the D1-D5 System September 2005 Masaki Shigemori (Caltech) hep-th/0508110: Vijay Balasubramanian, Per Kraus, M.S. 1. Introduction AdS/CFT Can

More information

Review of Statistical Mechanics

Review of Statistical Mechanics Review of Statistical Mechanics 3. Microcanonical, Canonical, Grand Canonical Ensembles In statistical mechanics, we deal with a situation in which even the quantum state of the system is unknown. The

More information

Fall 2004 Ali Shakouri

Fall 2004 Ali Shakouri University of California at Santa Cruz Jack Baskin School of Engineering Electrical Engineering Department EE-145L: Properties of Materials Laboratory Lab 5b: Temperature Dependence of Semiconductor Conductivity

More information

Non-Inductive Startup and Flux Compression in the Pegasus Toroidal Experiment

Non-Inductive Startup and Flux Compression in the Pegasus Toroidal Experiment Non-Inductive Startup and Flux Compression in the Pegasus Toroidal Experiment John B. O Bryan University of Wisconsin Madison NIMROD Team Meeting July 31, 2009 Outline 1 Introduction and Motivation 2 Modeling

More information

Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential 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 information

Topic 3. Evidence for the Big Bang

Topic 3. Evidence for the Big Bang Topic 3 Primordial nucleosynthesis Evidence for the Big Bang! Back in the 1920s it was generally thought that the Universe was infinite! However a number of experimental observations started to question

More information

Tutorial: Incorporating kinetic aspects of RF current drive in MHD simulation

Tutorial: Incorporating kinetic aspects of RF current drive in MHD simulation kinetic aspects of RF current with a focus on ECCD stabilization of tearing modes RF current Lorentz Workshop: Modeling Kinetic Aspects of Global MHD Modes 4 Dec 2013, Leiden, Netherlands Outline radio

More information

Heating & Cooling in Molecular Clouds

Heating & Cooling in Molecular Clouds Lecture 8: Cloud Stability Heating & Cooling in Molecular Clouds Balance of heating and cooling processes helps to set the temperature in the gas. This then sets the minimum internal pressure in a core

More information

Effective actions for fluids from holography

Effective actions for fluids from holography Effective actions for fluids from holography Based on: arxiv:1405.4243 and arxiv:1504.07616 with Michal Heller and Natalia Pinzani Fokeeva Jan de Boer, Amsterdam Benasque, July 21, 2015 (see also arxiv:1504.07611

More information

CLASSICAL CONCEPT REVIEW 8

CLASSICAL CONCEPT REVIEW 8 CLASSICAL CONCEPT REVIEW 8 Kinetic Theory Information concerning the initial motions of each of the atoms of macroscopic systems is not accessible, nor do we have the computational capability even with

More information

The properties of an ideal Fermi gas are strongly determined by the Pauli principle. We shall consider the limit: µ >> k B T βµ >> 1,

The properties of an ideal Fermi gas are strongly determined by the Pauli principle. We shall consider the limit: µ >> k B T βµ >> 1, Chapter 3 Ideal Fermi gas The properties of an ideal Fermi gas are strongly determined by the Pauli principle. We shall consider the limit: µ >> k B T βµ >>, which defines the degenerate Fermi gas. In

More information

Electric Dipole moments as probes of physics beyond the Standard Model

Electric 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 Non-Accelerator Particle Physics Group Indian Institute of Astrophysics Plan of the Talk Parity (P) and Time-reversal

More information

DIFFUSION IN SOLIDS. Materials often heat treated to improve properties. Atomic diffusion occurs during heat treatment

DIFFUSION IN SOLIDS. Materials often heat treated to improve properties. Atomic diffusion occurs during heat treatment DIFFUSION IN SOLIDS WHY STUDY DIFFUSION? Materials often heat treated to improve properties Atomic diffusion occurs during heat treatment Depending on situation higher or lower diffusion rates desired

More information

A Theory for the Cosmological Constant and its Explanation of the Gravitational Constant

A Theory for the Cosmological Constant and its Explanation of the Gravitational Constant A Theory for the Cosmological Constant and its Explanation of the Gravitational Constant H.M.Mok Radiation Health Unit, 3/F., Saiwanho Health Centre, Hong Kong SAR Govt, 8 Tai Hong St., Saiwanho, Hong

More information

arxiv:hep-ph/9902288v1 9 Feb 1999

arxiv:hep-ph/9902288v1 9 Feb 1999 A Quantum Field Theory Warm Inflation Model VAND-TH-98-01 Arjun Berera Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, USA arxiv:hep-ph/9902288v1 9 Feb 1999 Abstract A

More information

Notes on Polymer Rheology Outline

Notes on Polymer Rheology Outline 1 Why is rheology important? Examples of its importance Summary of important variables Description of the flow equations Flow regimes - laminar vs. turbulent - Reynolds number - definition of viscosity

More information

Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2)

Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) Lecture 3. Turbulent fluxes and TKE budgets (Garratt, Ch 2) In this lecture How does turbulence affect the ensemble-mean equations of fluid motion/transport? Force balance in a quasi-steady turbulent boundary

More information

HEAT UNIT 1.1 KINETIC THEORY OF GASES. 1.1.1 Introduction. 1.1.2 Postulates of Kinetic Theory of Gases

HEAT UNIT 1.1 KINETIC THEORY OF GASES. 1.1.1 Introduction. 1.1.2 Postulates of Kinetic Theory of Gases UNIT HEAT. KINETIC THEORY OF GASES.. Introduction Molecules have a diameter of the order of Å and the distance between them in a gas is 0 Å while the interaction distance in solids is very small. R. Clausius

More information

Widths of spectral lines

Widths of spectral lines Widths of spectral lines Real spectral lines are broadened because: Energy levels are not infinitely sharp. Atoms are moving relative to observer. 3 mechanisms determine profile φ(ν) Quantum mechanical

More information

Quark Model. Quark Model

Quark Model. Quark Model Quark odel Outline Hadrons Isosin Strangeness Quark odel Flavours u d s esons Pseudoscalar and vector mesons Baryons Deculet octet Hadron asses Sin-sin couling Heavy Quarks Charm bottom Heavy quark esons

More information

Nuclear Physics. Nuclear Physics comprises the study of:

Nuclear Physics. Nuclear Physics comprises the study of: Nuclear Physics Nuclear Physics comprises the study of: The general properties of nuclei The particles contained in the nucleus The interaction between these particles Radioactivity and nuclear reactions

More information

arxiv:hep-ph/0112027v1 3 Dec 2001

arxiv:hep-ph/0112027v1 3 Dec 2001 CERN-TH/2001-347 1 arxiv:hep-ph/0112027v1 3 Dec 2001 Strangeness and Statistical QCD Johann Rafelski a and Jean Letessier b a Department of Physics, University of Arizona, Tucson, AZ 85721 and CERN-Theory

More information

Lecture 12. Physical Vapor Deposition: Evaporation and Sputtering Reading: Chapter 12. ECE 6450 - Dr. Alan Doolittle

Lecture 12. Physical Vapor Deposition: Evaporation and Sputtering Reading: Chapter 12. ECE 6450 - Dr. Alan Doolittle Lecture 12 Physical Vapor Deposition: Evaporation and Sputtering Reading: Chapter 12 Evaporation and Sputtering (Metalization) Evaporation For all devices, there is a need to go from semiconductor to metal.

More information

SUPERCONDUCTIVITY. PH 318- Introduction to superconductors 1

SUPERCONDUCTIVITY. PH 318- Introduction to superconductors 1 SUPERCONDUCTIVITY property of complete disappearance of electrical resistance in solids when they are cooled below a characteristic temperature. This temperature is called transition temperature or critical

More information

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics

More information

Why 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. 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, A-800 Graz, Austria Abstract Chiral symmetry

More information

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 06 One-dimensional Gas Dynamics (Contd.) We

More information

6-2. A quantum system has the following energy level diagram. Notice that the temperature is indicated

6-2. A quantum system has the following energy level diagram. Notice that the temperature is indicated Chapter 6 Concept Tests 6-1. In a gas of hydrogen atoms at room temperature, what is the ratio of atoms in the 1 st excited energy state (n=2) to atoms in the ground state(n=1). (Actually H forms H 2 molecules,

More information

4 Microscopic dynamics

4 Microscopic dynamics 4 Microscopic dynamics In this section we will look at the first model that people came up with when they started to model polymers from the microscopic level. It s called the Oldroyd B model. We will

More information

arxiv:hep-ph/0309030v1 3 Sep 2003

arxiv:hep-ph/0309030v1 3 Sep 2003 arxiv:hep-ph/0309030v1 3 Sep 2003 Strangeness and Statistical Hadronization: How to Study Quark Gluon Plasma Jan Rafelski Department of Physics, University of Arizona, Tucson, AZ85721 and Jean Letessier

More information

fotoelektron-spektroszkópia Rakyta Péter

fotoelektron-spektroszkópia Rakyta Péter Spin-pálya kölcsönhatás grafénben, fotoelektron-spektroszkópia Rakyta Péter EÖTVÖS LORÁND TUDOMÁNYEGYETEM, KOMPLEX RENDSZEREK FIZIKÁJA TANSZÉK 1 Introduction to graphene Sp 2 hybridization p z orbitals

More information

Nuclear ZPE Tapping. Horace Heffner May 2007

Nuclear ZPE Tapping. Horace Heffner May 2007 ENERGY FROM UNCERTAINTY The uncertainty of momentum for a particle constrained by distance Δx is given, according to Heisenberg, by: Δmv = h/(2 π Δx) but since KE = (1/2) m v 2 = (1/(2 m) ) (Δmv) 2 ΔKE

More information

Bounding the Higgs width at the LHC

Bounding the Higgs width at the LHC Bounding the Higgs width at the LHC Higgs XSWG workshop, June 2014 John Campbell, Fermilab with K. Ellis, C. Williams 1107.5569, 1311.3589, 1312.1628 Reminder of the method This is the essence of the original

More information

0.33 d down 1 1. 0.33 c charm + 2 3. 0 0 1.5 s strange 1 3. 0 0 0.5 t top + 2 3. 0 0 172 b bottom 1 3

0.33 d down 1 1. 0.33 c charm + 2 3. 0 0 1.5 s strange 1 3. 0 0 0.5 t top + 2 3. 0 0 172 b bottom 1 3 Chapter 16 Constituent Quark Model Quarks are fundamental spin- 1 particles from which all hadrons are made up. Baryons consist of three quarks, whereas mesons consist of a quark and an anti-quark. There

More information

arxiv:hep-ph/0310021v2 4 Oct 2003

arxiv:hep-ph/0310021v2 4 Oct 2003 Physics in Collision - Zeuthen, Germany, June 6-8, 003 arxiv:hep-ph/0300v 4 Oct 003 SEARCHES FOR NEW PARTICLES AT THE ENERGY FRONTIER AT THE TEVATRON Patrice VERDIER LAL, Université Paris-Sud, 9898 Orsay

More information

3. Open Strings and D-Branes

3. Open Strings and D-Branes 3. Open Strings and D-Branes 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 information

4. Introduction to Heat & Mass Transfer

4. Introduction to Heat & Mass Transfer 4. Introduction to Heat & Mass Transfer This section will cover the following concepts: A rudimentary introduction to mass transfer. Mass transfer from a molecular point of view. Fundamental similarity

More information

1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids

1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids 1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.

More information

The Einstein field equations

The Einstein field equations The Einstein field equations Part I: the right-hand side Atle Hahn GFM, Universidade de Lisboa Lisbon, 21st January 2010 Contents: 1 Einstein field equations: overview 2 Special relativity: review 3 Classical

More information

1 Introduction. 1 There may, of course, in principle, exist other universes, but they are not accessible to our

1 Introduction. 1 There may, of course, in principle, exist other universes, but they are not accessible to our 1 1 Introduction Cosmology is the study of the universe as a whole, its structure, its origin, and its evolution. Cosmology is soundly based on observations, mostly astronomical, and laws of physics. These

More information

The MOS Transistor in Weak Inversion

The MOS Transistor in Weak Inversion MOFE Operation in eak and Moderate nversion he MO ransistor in eak nversion n this section we will lore the behavior of the MO transistor in the subthreshold regime where the channel is weakly inverted.

More information

- momentum conservation equation ρ = ρf. These are equivalent to four scalar equations with four unknowns: - pressure p - velocity components

- momentum conservation equation ρ = ρf. These are equivalent to four scalar equations with four unknowns: - pressure p - velocity components J. Szantyr Lecture No. 14 The closed system of equations of the fluid mechanics The above presented equations form the closed system of the fluid mechanics equations, which may be employed for description

More information

Non-Supersymmetric Seiberg Duality in orientifold QCD and Non-Critical Strings

Non-Supersymmetric Seiberg Duality in orientifold QCD and Non-Critical Strings Non-Supersymmetric Seiberg Duality in orientifold QCD and Non-Critical Strings, IAP Large N@Swansea, July 2009 A. Armoni, D.I., G. Moraitis and V. Niarchos, arxiv:0801.0762 Introduction IR dynamics of

More information

A i A i. µ(ion) = Z i X i

A i A i. µ(ion) = Z i X i Lecture 2 Review: calculation of mean atomic weight of an ionized gas (µ) Given a mass fraction X i (or abundance) for an ionic (or atomic) species with atomic weight A i, we can can calculate µ by: For

More information

Vortices at the A-B phase boundary in superfluid 3 He

Vortices at the A-B 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 information

Viscosity of Liquids: Methanol and Water

Viscosity of Liquids: Methanol and Water of Liquids: Methanol and Water Colin McGuire January 4 and February, 01 March, 01 1 1 Abstract This experiment was done in order to determine the viscosity of mixtures of methanol and water of concentrations

More information

Lecture 4 Classification of Flows. Applied Computational Fluid Dynamics

Lecture 4 Classification of Flows. Applied Computational Fluid Dynamics Lecture 4 Classification of Flows Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (00-006) Fluent Inc. (00) 1 Classification: fluid flow vs. granular flow

More information

Elliptical Galaxies. Houjun Mo. April 19, 2004. Basic properties of elliptical galaxies. Formation of elliptical galaxies

Elliptical Galaxies. Houjun Mo. April 19, 2004. Basic properties of elliptical galaxies. Formation of elliptical galaxies Elliptical Galaxies Houjun Mo April 19, 2004 Basic properties of elliptical galaxies Formation of elliptical galaxies Photometric Properties Isophotes of elliptical galaxies are usually fitted by ellipses:

More information

Ch 2 Properties of Fluids - II. Ideal Fluids. Real Fluids. Viscosity (1) Viscosity (3) Viscosity (2)

Ch 2 Properties of Fluids - II. Ideal Fluids. Real Fluids. Viscosity (1) Viscosity (3) Viscosity (2) Ch 2 Properties of Fluids - II Ideal Fluids 1 Prepared for CEE 3500 CEE Fluid Mechanics by Gilberto E. Urroz, August 2005 2 Ideal fluid: a fluid with no friction Also referred to as an inviscid (zero viscosity)

More information

Wave-particle and wave-wave interactions in the Solar Wind: simulations and observations

Wave-particle and wave-wave interactions in the Solar Wind: simulations and observations Wave-particle and wave-wave interactions in the Solar Wind: simulations and observations Lorenzo Matteini University of Florence, Italy In collaboration with Petr Hellinger, Simone Landi, and Marco Velli

More information

CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology

CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,

More information

Iterative calculation of the heat transfer coefficient

Iterative calculation of the heat transfer coefficient Iterative calculation of the heat transfer coefficient D.Roncati Progettazione Ottica Roncati, via Panfilio, 17 44121 Ferrara Aim The plate temperature of a cooling heat sink is an important parameter

More information

Stability of Evaporating Polymer Films. For: Dr. Roger Bonnecaze Surface Phenomena (ChE 385M)

Stability of Evaporating Polymer Films. For: Dr. Roger Bonnecaze Surface Phenomena (ChE 385M) Stability of Evaporating Polymer Films For: Dr. Roger Bonnecaze Surface Phenomena (ChE 385M) Submitted by: Ted Moore 4 May 2000 Motivation This problem was selected because the writer observed a dependence

More information