Transport in Conformal Quantum Fluids. Thomas Schaefer, North Carolina State University
|
|
- Myles Casey
- 5 years ago
- Views:
Transcription
1 Transport in Conformal Quantum Fluids Thomas Schaefer, North Carolina State University
2 Why study transport in (nearly perfect) quantum fluids? Transport without quasi-particles? Model system for QGP, strange metals, etc. Fluid dynamics is the universal effective description of non-equilibrium many body systems. Description is most effective in nearly perfect fluids. Fluid-gravity correspondence: Can (strongly coupled) fluids teach us something about quantum gravity?
3 Hydrodynamics Hydrodynamics (undergraduate version): Newton s law for continuous, deformable media.
4 Fluids: Gases, liquids, plasmas,... Hydrodynamics (postmodern): Effective theory of nonequilibrium long-wavelength, low-frequency dynamics of any many-body system. non conserved density conserved density τ τ micro τ λ τ τ micro : Dynamics of conserved charges. Water: (ρ, ɛ, π)
5 Not your grandfathers fluid Consider a many body system with σ 1/k 2 Can be made using Feshbach resonances in dilute atomic gases. Systems remains hydrodynamic despite expansion
6 Effective theories for fluids (Unitary Fermi Gas, T > T F ) L = ψ ( i M ) ψ C 0 2 (ψ ψ) 2 f p t + v x f p = C[f p ] ω < T t (ρv i) + x j Π ij = 0 ω < T s η
7 Effective theories (Strong coupling) L = λ(iσ D)λ 1 4 Ga µνg a µν +... S = 1 2κ 2 5 d 5 x gr +... SO(d + 2, 2) Schr 2 d AdS d+3 Schr 2 d t (ρv i) + x j Π ij = 0 (ω < T )
8 Outline I. EFT: Gradient expansion II. EFT: Fluctuations III. Models of fluids: Kinetic theory & QFT IV. Models of fluids: Holography V. Analyzing fluids: How to measure η/s VI. Analyzing fluids: How to measure D s
9 I. Gradient expansion (simple non-relativistic fluid) Simple fluid: Conservation laws for mass, energy, momentum ρ t + j ρ = 0 ɛ t + j ɛ = 0 π i t + x j Π ij = 0 Ward identity: mass current = momentum density j ρ ρ v = π Constitutive relations: Gradient expansion for currents Energy momentum tensor Π ij = P δ ij + ρv i v j + η ( i v j + j v i 23 ) δ ij k v k + O( 2 )
10 Conformal fluid dynamics: Symmetries Symmetries of a conformal non-relativistic fluid Galilean boost x = x + vt t = t Scale trafo x = e s x t = e 2s t Conformal trafo x = x/(1 + ct) 1/t = 1/t + c This is known as the Schrödinger algebra (= the symmetries of the free Schrödinger equation) Generators: Mass, momentum, angular momentum M = dx ρ P i = dx j i J ij = dx ɛ ijk x j j k Boost, dilations, special conformal K i = dx x i ρ D = dx x j C = dx x 2 ρ/2
11 Spurion method: Local symmetries Diffeomorphism invariance δx i = ξ i (x, t) δg ij = L ξ g ij = ξ k k g ij +... Gauge invariance δψ = iα(x, t)ψ δa 0 = α ξ k k A 0 A k ξk δa i = i α ξ k k A i A k i ξ k + mg ik ξk Conformal transformations δt = β(t) δo = βȯ 1 2 βo O More recent work: Newton-Cartan geometry Son, Wingate (2006), Jensen (2014)
12 Example: Stress tensor Determine transformation properties of fluid dynamic variables δρ = L ξ ρ δs = L ξ s δv = L ξ v + ξ Stress tensor: Ideal fluid dynamics Π 0 ij = P g ij + ρv i v j, P = 2 3 E First order viscous hydrodynamics δ (1) Π ij = ησ ij ζg ij σ ζ = 0 σ ij = ( i v j + j v i + ġ ij 2 ) 3 g ij σ σ = v + ġ 2g Son (2007)
13 Simple application: Kubo formula Consider background metric g ij (t, x) = δ ij + h ij (t, x). Linear response δπ xy = 1 2 Gxyxy R h xy Harmonic perturbation h xy = h 0 e iωt Kubo relation: G xyxy R = P iηω +... η = lim ω 0 [ 1 ω ImGxyxy R (ω, 0) Gradient expansion: ω P η s η T. ]
14 II. Beyond gradients: Hydrodynamic fluctuations Hydrodynamic variables fluctuate δv i (x, t)δv j (x, t) = T ρ δ ijδ(x x ) Linearized hydrodynamics propagates fluctuations as shear or sound δvi T δvj T ω,k = 2T ρ (δ ij ˆk νk 2 iˆkj ) ω 2 + (νk 2 ) 2 δv L i δv L j ω,k = 2T ρ ˆk iˆkj shear ωk 2 Γ (ω 2 c 2 sk 2 ) 2 + (ωk 2 Γ) 2 sound v = v T + v L : v T = 0, v L = 0 ν = η/ρ, Γ = 4 3 ν +...
15 Hydro Loops: Breakdown of second order hydro Correlation function in hydrodynamics G xyxy S = {Π xy, Π xy } ω,k ρ 2 0 {v x v y, v x v y } ω,k v T ρ ρ v T vl v L v L ρ ρ ρ vt Match to response function in ω 0 (Kubo) limit ρ G xyxy R = P + δp iω[η + δη] + ω 2 [ητ π + δ(ητ π )] with δp T Λ 3 δη T ρλ η δ(ητ π ) 1 ω T ρ 3/2 η 3/2
16 Hydro Loops: RG and breakdown of 2nd order hydro Cutoff dependence can be absorbed into bare parameters. Non-analytic terms are cutoff independent. Fluid dynamics is a renormalizable effective theory. ( ) 2 ( ρ P Small η enhances fluctuation corrections: δη T η ρ ) 1/2 Small η leads to large δη: There must be a bound on η/n. Relaxation time diverges: δ(ητ π ) 1 ω ( ρ η ) 3/2 2nd order hydro without fluctuations inconsistent.
17 Fluctuation induced bound on η/s η/s η(ω)/s 0.20 fluctuations (η/s) min kinetic theory T/T F ω/t F spectral function non-analytic ω term Schaefer, Chafin (2012), see also Kovtun, Moore, Romatschke (2011)
18 IIIa. Kinetic theory Microscopic picture: Quasi-particle distribution function f p (x, t) ρ(x, t) = dγ p gmfp (x, t) π i (x, t) = dγ p gpi f p (x, t) Π ij (x, t) = dγ p gpi v j f p (x, t) Boltzmann equation ( t + pi m x i ( g il ġ lj p j + Γ i p j p k ) ) jk m p i f p (t, x, ) = C[f] C[f] = Solve order-by-order in Knudsen number Kn = l mfp /L
19 Kinetic theory: Knudsen expansion Chapman-Enskog expansion f = f 0 + δf 1 + δf Gradient exp. δf n = O( n ) Knudsen exp. δf n = O(Kn n ) First order result Bruun, Smith (2005) δ (1) Π ij = ησ ij η = (mt )3/2 π Second order result Chao, Schaefer (2012), Schaefer (2014) [ δ (2) Π ij = η2 Dσ ij + 2 ] P 3 σij ( v) + η2 P [ ] σ i k σj k σ i k Ωj k + O(κη i j T ) relaxation time τ π = η/p
20 Frequency dependence, breakdown of kinetic theory Consider harmonic perturbation h xy e iωt+ikx. Use schematic collision term C[f 0 p + δf p ] = δf p /τ. δf p (ω, k) = 1 2T iωp x v y iω + i v k + τ 1 0 Leads to Lorentzian line shape of transport peak f 0 p h xy. η(ω) = η(0) 1 + ω 2 τ 2 0 Pole at ω = iτ 1 0 (τ 0 = η/(st )) controls range of convergence of gradient expansion. High frequency behavior misses short range correlations for ω > T.
21 IIIb. Quantum Field Theory = The diagrammatic content of the Boltzmann equation is known: Kubo formula with Maki-Thompson + Azlamov-Larkin + Self-energy Can be used to extrapolate Boltzmann result to T T F viscosity η [ h n] classical 2.77 T 3/2 viscosity η(ω=0) T [T F ] η(ω) [ h n] ω [E F / h] T=10 T= 5 T= 2 T= 1 T=0.5 T=0.151 Enss, Zwerger (2011), see also Levin (2014)
22 Operator product expansion (OPE) Short time behavior: OPE η(ω) = n O n ω ( n d)/2 O n (λ 2 t, λx) = λ n O n (t, x) Leading operator: Contact density (Tan) O C = C 2 0ψψψ ψ = ΦΦ C = 4 η(ω) O C / ω. Asymptotic behavior + analyticity gives sum rule [ 1 dw η(ω) O ] C π 15π = E mω 3 Randeria, Taylor (2010), Enss, Zwerger (2011), Hoffman (2013)
23 IV. Holography DLCQ idea: Light cone compactification of relativistic theory in d+2 p µ p µ = 2p + p p 2 = 0 p = p2 p + = 2n + 1 2p + L Galilean invariant theory in d+1 dimensions. String theory embedding: Null Melvin Twist AdS d+3 NMT Schr 2 d Iso(AdS d+3 ) = SO(d + 2, 2) Schr(d) Son (2008), Balasubramanian et al. (2008) Other ideas: Horava-Lifshitz (Karch, 2013)
24 Schrödinger Metric Fluctuations δg y x = e iωu χ(ω, r) satisfy wave equation (u = (r + /r) 2 ) χ (ω, u) 1 + u2 f(u)u χ (ω, u) + u f(u) 2 w2 χ(ω, u) = 0 Retarded correlation function G R (ω) = βr3 + v f(u)χ (ω, u) 4πG 5 uχ(ω, u). u 0 Viscosity from Kubo relation η s = 1 4π Adams et al. (2008), Herzog et al. (2008)
25 Spectral function η(ω)/s η(0)/s = 1/(4π) η(ω ) ω 1/ ω/(πt ) Kubo relation (incl. τ π ): G R (ω) = P iηω + τ π ηω 2 + κ R k 2 τ π T = log(2) 2π AdS 5 : τ π T = 2 log(2) 2π Range of validity of fluid dynamics: ω < T Sch 2 : Cannot be matched to relaxation type hydro? Schaefer (2014), BRSSS (2008)
26 Quasi-normal modes Re w Re w Im w 4 Im w Sch 2 2 AdS 5 QNM s are stable, Im λ < 0. Pole at ω it limits convergence of fluid dynamics. Modes overdamped in Sch 2 2. Schaefer (2014), Starinets (2002), Heller (2012)
27 V. Experiments: Elliptic flow σ σ µ Hydrodynamic expansion converts coordinate space anisotropy to momentum space anisotropy σ σ O Hara et al. (2002)
28 Determination of η(n, T ) Measurement of A R (t, E 0 ) determines η(n, T ). But: gas n(x) fluid The whole cloud is not a fluid. Can we ignore this issue? v(x) transition regime heat current viscous stress δπ( x) No. Hubble flow & low density viscosity η T 3/2 lead to paradoxical fluid dynamics. Q = σ δπ =
29 Possible Solutions Combine hydrodynamics & Boltzmann equation. Not straightforward. Hydrodynamics + non-hydro degrees of freedom (E a ; a = x, y, z) E a t + j a ɛ = P a 2τ E t + j ɛ = 0 P a = P a P E = a E a τ small: Fast relaxation to Navier-Stokes with τ = η/p τ large: Additional conservation laws. Ballistic expansion.
30 Anisotropic Hydrodynamics: Comparison with Boltzmann Aspect ratio A R (t) = ( r 2 / r2 z ) 1/2 (T/T F = 0.79, 1.11, 1.54) Dots: Two-body Boltzmann equation with full collision kernel Lines: Anisotropic hydro with η fixed by Chapman-Enskog High temperature (dilute) limit: Perfect agreement! Boltzmann, Pantel et al (2015); AVH1 hydro code, M. Bluhm & T.S. (2015)
31 Elliptic flow: High T limit Quantum viscosity η = η 0 (mt ) 3/2 2 T /T F = 0.79, 1.11, 1.54 Cao et al., Science (2010) Bluhm et al., PRL (2016) fit: η 0 = ± 0.02 theory: η 0 = π = 0.269
32 Anisotropic fluid dynamics analysis AR(t * ) E/(NE F ) A R = σx/σy as function of total energy. Data: Joseph et al (2016). E/(NE F ) 0.6 is the superfluid transition. Grey, Blue, Green: LO, NLO, NNLO fit. η = η 0 (mt ) 3/2 { 1 + η 2 nλ 3 + η 3 (nλ 3 ) }
33 Reconstruct η/n and η/s η/n 4 η/s T/T F T/T F Left: η/n (Red band) Right: η/s (Red band) Tc 0.17T F. Joseph et al. (Black points). Enss et al. (Dashed line). Kinetic theory at low and high T (blue dashed) η(t T c ) = (0.265 ± 0.02)(mT ) 3/2 η 0 (th) = π = η/n Tc = 0.41 ± 0.15 η/s Tc = 0.56 ± 0.20
34 VI. Spin Diffusion md s /ħ T/T F Simple scaling at high T ( T ) 3/2 P exp( Γt) Γ s ω2 z Γ D S = 6.3 m T F Sommer et al. (2011) Theory predicts Ds = 1.1( /m)(t /T F ) 3/2, Bruun (2010), Sommer et al. (2011)
35 Spin Diffusion at high temperature Kinetic theory (T > T f ) D 1/n Get large spin current j s D M in dilute corona. Predict spin drag Γ s 1.8E F (0) Γ red ( TF T ) 1/2 with Γ red > 200. Experiment 11.3 z ρ
36 Spin Hydrodynamics d z d z t t Crossover from ballistic to diffusive behavior for D const Decay of spin dipole mode for diffusion constant D 1/n D = β, β = (1000, 5, 2, 1, 0.05) D = β T (mt ) 3/2 /n, β T = (0.2, 0.1, 0.05, 0.02) Find Γ red 11.0, in agreement with experiment
37 Time to pour yourself a good fluid Questions to ponder: Fluid dynamics as an E(F)T? Unfold temperature, density dependence of η/s, D s and κ. Best way to do hydro+? LBE, stoch hydro. Ahydro, Quasi-particles or quasi-normal modes?
38 Appendix I: Beyond conformal symmetry
39 Bulk viscosity and conformal symmetry breaking Conformal symmetry breaking (thermodynamics) 1 2E 3P = O C 12πmaP 1 6π nλ3 λ a How does this translate into ζ 0? Momentum dependent m (p). Bulk viscosity ζ = π λ 3 ( zλ a Im Σ(k) zt Re Σ(k) zt λ a T ɛ k Erf T ɛ k F D ) 2 ζ ( 1 2E 3P ( ɛk T ) ( ɛk ) 2 η T T )
40 Shear viscosity and conformal symmetry breaking Consider shear viscosity at a ( ) λ 2 η = η 0 {1 + O a 2 + O ( ) zλ a } +... Medium effects at O(zλ/a): Self energy, in-medium scattering Π(P, q) = η/η t = 1 t = 2 t = /(k F a) Minimum shear viscosity achieved on BEC side Bluhm, Schaefer (2014)
Fluid dynamics for the unitary Fermi gas. Thomas Schaefer, North Carolina State University
Fluid dynamics for the unitary Fermi gas Thomas Schaefer, North Carolina State University Non-relativistic fermions in unitarity limit Consider simple square well potential a < 0 a =, ǫ B = 0 a > 0, ǫ
More informationConformal Quantum Fluids. Thomas Schaefer, North Carolina State University
Conformal Quantum Fluids Thomas Schaefer, North Carolina State University Why study (nearly perfect) quantum fluids? Hard computational problem: Have to determine real time correlation functions. Achieve
More information(Non) Conformal Quantum Fluids. Thomas Schaefer, North Carolina State University
(Non) Conformal Quantum Fluids Thomas Schaefer, North Carolina State University Why study (nearly perfect) quantum fluids? Hard computational problem: Have to determine real time correlation functions.
More informationAnisotropic fluid dynamics. Thomas Schaefer, North Carolina State University
Anisotropic fluid dynamics Thomas Schaefer, North Carolina State University Outline We wish to extract the properties of nearly perfect (low viscosity) fluids from experiments with trapped gases, colliding
More informationFluid dynamics as an effective theory. Thomas Schaefer, North Carolina State University
Fluid dynamics as an effective theory Thomas Schaefer, North Carolina State University Hydroynamics Hydrodynamics (undergraduate version): Newton s law for continuous, deformable media. Fluids: Gases,
More information(Nearly) Scale invariant fluid dynamics for the dilute Fermi gas in two and three dimensions. Thomas Schaefer North Carolina State University
(Nearly) Scale invariant fluid dynamics for the dilute Fermi gas in two and three dimensions Thomas Schaefer North Carolina State University Outline I. Conformal hydrodynamics II. Observations (3d) III.
More information(Super) Fluid Dynamics. Thomas Schaefer, North Carolina State University
(Super) Fluid Dynamics Thomas Schaefer, North Carolina State University Hydrodynamics Hydrodynamics (undergraduate version): Newton s law for continuous, deformable media. Fluids: Gases, liquids, plasmas,...
More information(Nearly) perfect fluidity in cold atomic gases: Recent results. Thomas Schaefer North Carolina State University
(Nearly) perfect fluidity in cold atomic gases: Recent results Thomas Schaefer North Carolina State University Fluids: Gases, Liquids, Plasmas,... Hydrodynamics: Long-wavelength, low-frequency dynamics
More informationScale invariant fluid dynamics for the dilute Fermi gas at unitarity
Scale invariant fluid dynamics for the dilute Fermi gas at unitarity Thomas Schaefer North Carolina State University Fluids: Gases, Liquids, Plasmas,... Hydrodynamics: Long-wavelength, low-frequency dynamics
More informationNearly Perfect Fluidity: From Cold Atoms to Hot Quarks. Thomas Schaefer, North Carolina State University
Nearly Perfect Fluidity: From Cold Atoms to Hot Quarks Thomas Schaefer, North Carolina State University RHIC serves the perfect fluid Experiments at RHIC are consistent with the idea that a thermalized
More informationQuantum limited spin transport in ultracold atomic gases
Quantum limited spin transport in ultracold atomic gases Searching for the perfect SPIN fluid... Tilman Enss (Uni Heidelberg) Rudolf Haussmann (Uni Konstanz) Wilhelm Zwerger (TU München) Technical University
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 informationStrongly interacting quantum fluids: Transport theory
Strongly interacting quantum fluids: Transport theory Thomas Schaefer North Carolina State University Fluids: Gases, Liquids, Plasmas,... Hydrodynamics: Long-wavelength, low-frequency dynamics of conserved
More informationIntersections of nuclear physics and cold atom physics
Intersections of nuclear physics and cold atom physics Thomas Schaefer North Carolina State University Unitarity limit Consider simple square well potential a < 0 a =, ǫ B = 0 a > 0, ǫ B > 0 Unitarity
More informationNon-relativistic AdS/CFT
Non-relativistic AdS/CFT Christopher Herzog Princeton October 2008 References D. T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry, Phys. Rev. D 78,
More informationLifshitz Hydrodynamics
Lifshitz Hydrodynamics Yaron Oz (Tel-Aviv University) With Carlos Hoyos and Bom Soo Kim, arxiv:1304.7481 Outline Introduction and Summary Lifshitz Hydrodynamics Strange Metals Open Problems Strange Metals
More informationCold atoms and AdS/CFT
Cold atoms and AdS/CFT D. T. Son Institute for Nuclear Theory, University of Washington Cold atoms and AdS/CFT p.1/27 History/motivation BCS/BEC crossover Unitarity regime Schrödinger symmetry Plan Geometric
More informationGauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger. Julius-Maximilians-Universität Würzburg
Gauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger Julius-Maximilians-Universität Würzburg 1 New Gauge/Gravity Duality group at Würzburg University Permanent members 2 Gauge/Gravity
More informationTransport coefficients from Kinetic Theory: Bulk viscosity, Diffusion, Thermal conductivity. Debarati Chatterjee
Transport coefficients from Kinetic Theory: Bulk viscosity, Diffusion, Thermal conductivity Debarati Chatterjee Recap: Hydrodynamics of nearly perfect fluids Hydrodynamics: correlation functions at low
More informationCollaborators: Aleksas Mazeliauskas (Heidelberg) & Derek Teaney (Stony Brook) Refs: , /25
2017 8 28 30 @ Collaborators: Aleksas Mazeliauskas (Heidelberg) & Derek Teaney (Stony Brook) Refs: 1606.07742, 1708.05657 1/25 1. Introduction 2/25 Ultra-relativistic heavy-ion collisions and the Bjorken
More informationTowards new relativistic hydrodynamcis from AdS/CFT
Towards new relativistic hydrodynamcis from AdS/CFT Michael Lublinsky Stony Brook with Edward Shuryak QGP is Deconfined QGP is strongly coupled (sqgp) behaves almost like a perfect liquid (Navier-Stokes
More informationViscosity in strongly coupled gauge theories Lessons from string theory
Viscosity in strongly coupled gauge theories Lessons from string theory Pavel Kovtun KITP, University of California, Santa Barbara A.Buchel, (University of Western Ontario) C.Herzog, (University of Washington,
More informationThe critical point in QCD
The critical point in QCD Thomas Scha fer North Carolina State University The phase diagram of QCD L = q f (id/ m f )q f 1 4g 2 Ga µνg a µν 2000: Dawn of the collider era at RHIC Au + Au @200 AGeV What
More informationHydrodynamics. Stefan Flörchinger (Heidelberg) Heidelberg, 3 May 2010
Hydrodynamics Stefan Flörchinger (Heidelberg) Heidelberg, 3 May 2010 What is Hydrodynamics? Describes the evolution of physical systems (classical or quantum particles, fluids or fields) close to thermal
More informationQuark-gluon plasma from AdS/CFT Correspondence
Quark-gluon plasma from AdS/CFT Correspondence Yi-Ming Zhong Graduate Seminar Department of physics and Astronomy SUNY Stony Brook November 1st, 2010 Yi-Ming Zhong (SUNY Stony Brook) QGP from AdS/CFT Correspondence
More informationProbing Universality in AdS/CFT
1 / 24 Probing Universality in AdS/CFT Adam Ritz University of Victoria with P. Kovtun [0801.2785, 0806.0110] and J. Ward [0811.4195] Shifmania workshop Minneapolis May 2009 2 / 24 Happy Birthday Misha!
More informationHolography for non-relativistic CFTs
Holography for non-relativistic CFTs Herzog, Rangamani & SFR, 0807.1099, Rangamani, Son, Thompson & SFR, 0811.2049, SFR & Saremi, 0907.1846 Simon Ross Centre for Particle Theory, Durham University Liverpool
More informationHydrodynamic Modes of Incoherent Black Holes
Hydrodynamic Modes of Incoherent Black Holes Vaios Ziogas Durham University Based on work in collaboration with A. Donos, J. Gauntlett [arxiv: 1707.xxxxx, 170x.xxxxx] 9th Crete Regional Meeting on String
More informationApplications of AdS/CFT correspondence to cold atom physics
Applications of AdS/CFT correspondence to cold atom physics Sergej Moroz in collaboration with Carlos Fuertes ITP, Heidelberg Outline Basics of AdS/CFT correspondence Schrödinger group and correlation
More informationCold atoms and AdS/CFT
Cold atoms and AdS/CFT D. T. Son Institute for Nuclear Theory, University of Washington Cold atoms and AdS/CFT p.1/20 What is common for strong coupled cold atoms and QGP? Cold atoms and AdS/CFT p.2/20
More informationAdS/CFT and condensed matter physics
AdS/CFT and condensed matter physics Simon Ross Centre for Particle Theory, Durham University Padova 28 October 2009 Simon Ross (Durham) AdS/CMT 28 October 2009 1 / 23 Outline Review AdS/CFT Application
More informationUniversal Quantum Viscosity in a Unitary Fermi Gas
Universal Quantum Viscosity in a Unitary Fermi Gas Chenglin Cao Duke University July 5 th, 011 Advisor: Prof. John E Thomas Dr.Ilya Arakelyan Dr.James Joseph Dr.Haibin Wu Yingyi Zhang Ethan Elliott Willie
More informationIn this chapter we will discuss the effect of shear viscosity on evolution of fluid, p T
Chapter 3 Shear viscous evolution In this chapter we will discuss the effect of shear viscosity on evolution of fluid, p T spectra, and elliptic flow (v ) of pions using a +1D relativistic viscous hydrodynamics
More informationTrans-series & hydrodynamics far from equilibrium
Trans-series & hydrodynamics far from equilibrium Michal P. Heller Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Germany National Centre for Nuclear Research, Poland many
More informationRecent lessons about hydrodynamics from holography
Recent lessons about hydrodynamics from holography Michał P. Heller m.p.heller@uva.nl University of Amsterdam, The Netherlands & National Centre for Nuclear Research, Poland (on leave) based on 03.3452
More informationUniversal quantum transport in ultracold Fermi gases
Universal quantum transport in ultracold Fermi gases How slowly can spins diffuse? Tilman Enss (U Heidelberg) Rudolf Haussmann (U Konstanz) Wilhelm Zwerger (TU München) Aarhus, 26 June 24 Transport in
More informationarxiv: v1 [nucl-th] 9 Jun 2008
Dissipative effects from transport and viscous hydrodynamics arxiv:0806.1367v1 [nucl-th] 9 Jun 2008 1. Introduction Denes Molnar 1,2 and Pasi Huovinen 1 1 Purdue University, Physics Department, 525 Northwestern
More informationQGP, Hydrodynamics and the AdS/CFT correspondence
QGP, Hydrodynamics and the AdS/CFT correspondence Adrián Soto Stony Brook University October 25th 2010 Adrián Soto (Stony Brook University) QGP, Hydrodynamics and AdS/CFT October 25th 2010 1 / 18 Outline
More informationGerry and Fermi Liquid Theory. Thomas Schaefer North Carolina State
Ë Ë Ë³ Gerry and Fermi Liquid Theory Thomas Schaefer North Carolina State Introduction I learned about Fermi liquid theory (FLT from Gerry. I was under the imression that the theory amounted to the oeration
More informationDivergence of the gradient expansion and the applicability of fluid dynamics Gabriel S. Denicol (IF-UFF)
Divergence of the gradient expansion and the applicability of fluid dynamics Gabriel S. Denicol (IF-UFF) arxiv:1608.07869, arxiv:1711.01657, arxiv:1709.06644 Frankfurt University 1.February.2018 Preview
More informationEquilibrium and nonequilibrium properties of unitary Fermi gas from Quantum Monte Carlo
Equilibrium and nonequilibrium properties of unitary ermi gas from Quantum Monte Carlo Piotr Magierski Warsaw University of Technology Collaborators: A. Bulgac - University of Washington J.E. Drut - University
More informationHolography and (Lorentzian) black holes
Holography and (Lorentzian) black holes Simon Ross Centre for Particle Theory The State of the Universe, Cambridge, January 2012 Simon Ross (Durham) Holography and black holes Cambridge 7 January 2012
More informationTheory of metallic transport in strongly coupled matter. 4. Magnetotransport. Andrew Lucas
Theory of metallic transport in strongly coupled matter 4. Magnetotransport Andrew Lucas Stanford Physics Geometry and Holography for Quantum Criticality; Asia-Pacific Center for Theoretical Physics August
More informationViscosity Correlators in Improved Holographic QCD
Bielefeld University October 18, 2012 based on K. Kajantie, M.K., M. Vepsäläinen, A. Vuorinen, arxiv:1104.5352[hep-ph]. K. Kajantie, M.K., A. Vuorinen, to be published. 1 Motivation 2 Improved Holographics
More informationThermo-electric transport in holographic systems with moment
Thermo-electric Perugia 2015 Based on: Thermo-electric gauge/ models with, arxiv:1406.4134, JHEP 1409 (2014) 160. Analytic DC thermo-electric conductivities in with gravitons, arxiv:1407.0306, Phys. Rev.
More informationNon-relativistic holography
University of Amsterdam AdS/CMT, Imperial College, January 2011 Why non-relativistic holography? Gauge/gravity dualities have become an important new tool in extracting strong coupling physics. The best
More informationHydrodynamical description of ultrarelativistic heavy-ion collisions
Frankfurt Institute for Advanced Studies June 27, 2011 with G. Denicol, E. Molnar, P. Huovinen, D. H. Rischke 1 Fluid dynamics (Navier-Stokes equations) Conservation laws momentum conservation Thermal
More informationHydrodynamics and QCD Critical Point in Magnetic Field
Hydrodynamics and QCD Critical Point in Magnetic Field University of Illinois at Chicago May 25, 2018 INT Workshop Multi Scale Problems Using Effective Field Theories Reference: Phys.Rev. D97 (2018) no.5,
More informationOn the effective action in hydrodynamics
On the effective action in hydrodynamics Pavel Kovtun, University of Victoria arxiv: 1502.03076 August 2015, Seattle Outline Introduction Effective action: Phenomenology Effective action: Bottom-up Effective
More informationQuantum gases in the unitary limit and...
Quantum gases in the unitary limit and... Andre LeClair Cornell university Benasque July 2 2010 Outline The unitary limit of quantum gases S-matrix based approach to thermodynamics Application to the unitary
More informationHadronic equation of state and relativistic heavy-ion collisions
Hadronic equation of state and relativistic heavy-ion collisions Pasi Huovinen J. W. Goethe Universität Workshop on Excited Hadronic States and the Deconfinement Transition Feb 23, 2011, Thomas Jefferson
More informationCollective Effects. Equilibrium and Nonequilibrium Physics
Collective Effects in Equilibrium and Nonequilibrium Physics: Lecture 3, 3 March 2006 Collective Effects in Equilibrium and Nonequilibrium Physics Website: http://cncs.bnu.edu.cn/mccross/course/ Caltech
More informationRelativistic magnetotransport in graphene
Relativistic magnetotransport in graphene Markus Müller in collaboration with Lars Fritz (Harvard) Subir Sachdev (Harvard) Jörg Schmalian (Iowa) Landau Memorial Conference June 6, 008 Outline Relativistic
More informationStrongly interacting quantum fluids: Experimental status
Strongly interacting quantum fluids: Experimental status Thomas Schaefer North Carolina State University Perfect fluids: The contenders QGP (T=180 MeV) Liquid Helium (T=0.1 mev) Trapped Atoms (T=0.1 nev)
More informationFefferman Graham Expansions for Asymptotically Schroedinger Space-Times
Copenhagen, February 20, 2012 p. 1/16 Fefferman Graham Expansions for Asymptotically Schroedinger Space-Times Jelle Hartong Niels Bohr Institute Nordic String Theory Meeting Copenhagen, February 20, 2012
More informationThe Phases of QCD. Thomas Schaefer. North Carolina State University
The Phases of QCD Thomas Schaefer North Carolina State University 1 Plan of the lectures 1. QCD and States of Matter 2. The High Temperature Phase: Theory 3. Exploring QCD at High Temperature: Experiment
More informationGeometric responses of Quantum Hall systems
Geometric responses of Quantum Hall systems Alexander Abanov December 14, 2015 Cologne Geometric Aspects of the Quantum Hall Effect Fractional Quantum Hall state exotic fluid Two-dimensional electron gas
More informationQuick Recapitulation of Fluid Mechanics
Quick Recapitulation of Fluid Mechanics Amey Joshi 07-Feb-018 1 Equations of ideal fluids onsider a volume element of a fluid of density ρ. If there are no sources or sinks in, the mass in it will change
More informationUnitary Fermi Gas: Quarky Methods
Unitary Fermi Gas: Quarky Methods Matthew Wingate DAMTP, U. of Cambridge Outline Fermion Lagrangian Monte Carlo calculation of Tc Superfluid EFT Random matrix theory Fermion L Dilute Fermi gas, 2 spins
More informationOne-loop renormalization in a toy model of Hořava-Lifshitz gravity
1/0 Università di Roma TRE, Max-Planck-Institut für Gravitationsphysik One-loop renormalization in a toy model of Hořava-Lifshitz gravity Based on (hep-th:1311.653) with Dario Benedetti Filippo Guarnieri
More informationHydrodynamical Model and Shear Viscosity from Black Holes (η/s from AdS/CFT)
Hydrodynamical Model and Shear Viscosity from Black Holes (η/s from AdS/CFT) Klaus Reygers / Kai Schweda Physikalisches Institut University of Heidelberg Space-time evolution QGP life time 10 fm/c 3 10-23
More informationChapter 4. COSMOLOGICAL PERTURBATION THEORY
Chapter 4. COSMOLOGICAL PERTURBATION THEORY 4.1. NEWTONIAN PERTURBATION THEORY Newtonian gravity is an adequate description on small scales (< H 1 ) and for non-relativistic matter (CDM + baryons after
More informationHydrodynamics, Thermodynamics, and Mathematics
Hydrodynamics, Thermodynamics, and Mathematics Hans Christian Öttinger Department of Mat..., ETH Zürich, Switzerland Thermodynamic admissibility and mathematical well-posedness 1. structure of equations
More informationTermodynamics and Transport in Improved Holographic QCD
Termodynamics and Transport in Improved Holographic QCD p. 1 Termodynamics and Transport in Improved Holographic QCD Francesco Nitti APC, U. Paris VII Large N @ Swansea July 07 2009 Work with E. Kiritsis,
More informationStatus of Hořava Gravity
Status of Institut d Astrophysique de Paris based on DV & T. P. Sotiriou, PRD 85, 064003 (2012) [arxiv:1112.3385 [hep-th]] DV & T. P. Sotiriou, JPCS 453, 012022 (2013) [arxiv:1212.4402 [hep-th]] DV, arxiv:1502.06607
More informationHolographic transport with random-field disorder. Andrew Lucas
Holographic transport with random-field disorder Andrew Lucas Harvard Physics Quantum Field Theory, String Theory and Condensed Matter Physics: Orthodox Academy of Crete September 1, 2014 Collaborators
More informationHydrodynamics in the Dirac fluid in graphene. Andrew Lucas
Hydrodynamics in the Dirac fluid in graphene Andrew Lucas Stanford Physics Fluid flows from graphene to planet atmospheres; Simons Center for Geometry and Physics March 20, 2017 Collaborators 2 Subir Sachdev
More informationLectures on gauge-gravity duality
Lectures on gauge-gravity duality Annamaria Sinkovics Department of Applied Mathematics and Theoretical Physics Cambridge University Tihany, 25 August 2009 1. Review of AdS/CFT i. D-branes: open and closed
More informationFinite Temperature Field Theory
Finite Temperature Field Theory Dietrich Bödeker, Universität Bielefeld 1. Thermodynamics (better: thermo-statics) (a) Imaginary time formalism (b) free energy: scalar particles, resummation i. pedestrian
More informationEuler equation and Navier-Stokes equation
Euler equation and Navier-Stokes equation WeiHan Hsiao a a Department of Physics, The University of Chicago E-mail: weihanhsiao@uchicago.edu ABSTRACT: This is the note prepared for the Kadanoff center
More informationBoost-invariant dynamics near and far from equilibrium physics and AdS/CFT.
Boost-invariant dynamics near and far from equilibrium physics and AdS/CFT. Micha l P. Heller michal.heller@uj.edu.pl Department of Theory of Complex Systems Institute of Physics, Jagiellonian University
More informationTalk based on: arxiv: arxiv: arxiv: arxiv: arxiv:1106.xxxx. In collaboration with:
Talk based on: arxiv:0812.3572 arxiv:0903.3244 arxiv:0910.5159 arxiv:1007.2963 arxiv:1106.xxxx In collaboration with: A. Buchel (Perimeter Institute) J. Liu, K. Hanaki, P. Szepietowski (Michigan) The behavior
More informationHolography with Shape Dynamics
. 1/ 11 Holography with Henrique Gomes Physics, University of California, Davis July 6, 2012 In collaboration with Tim Koslowski Outline 1 Holographic dulaities 2 . 2/ 11 Holographic dulaities Ideas behind
More informationTemperature dependence of shear viscosity of SU(3) gluodynamics within lattice simulation
Temperature dependence of shear viscosity of SU(3) gluodynamics within lattice simulation V.V. Braguta ITEP 20 April, 2017 Outline: Introduction Details of the calculation Shear viscocity Fitting of the
More informationTheory of Cosmological Perturbations
Theory of Cosmological Perturbations Part III CMB anisotropy 1. Photon propagation equation Definitions Lorentz-invariant distribution function: fp µ, x µ ) Lorentz-invariant volume element on momentum
More informationFluid dynamics of electrons in graphene. Andrew Lucas
Fluid dynamics of electrons in graphene Andrew Lucas Stanford Physics Condensed Matter Seminar, Princeton October 17, 2016 Collaborators 2 Subir Sachdev Harvard Physics & Perimeter Institute Philip Kim
More informationTASI lectures: Holography for strongly coupled media
TASI lectures: Holography for strongly coupled media Dam T. Son Below is only the skeleton of the lectures, containing the most important formulas. I. INTRODUCTION One of the main themes of this school
More informationChiral Magnetic and Vortical Effects at Weak Coupling
Chiral Magnetic and Vortical Effects at Weak Coupling University of Illinois at Chicago and RIKEN-BNL Research Center June 19, 2014 XQCD 2014 Stonybrook University, June 19-20, 2014 Chiral Magnetic and
More informationThe Superfluid-Insulator transition
The Superfluid-Insulator transition Boson Hubbard model M.P. A. Fisher, P.B. Weichmann, G. Grinstein, and D.S. Fisher, Phys. Rev. B 40, 546 (1989). Superfluid-insulator transition Ultracold 87 Rb atoms
More informationSecond-Order Relativistic Hydrodynamics
Second-Order Relativistic Hydrodynamics Guy D. Moore, Mark York, Kiyoumars Sohrabi, Paul Romatschke, Pavel Kovtun Why do we want to do relativistic Hydro? Why second order hydro, and what are coefficients?
More informationApplied Newton-Cartan Geometry: A Pedagogical Review
Applied Newton-Cartan Geometry: A Pedagogical Review Eric Bergshoeff Groningen University 10th Nordic String Meeting Bremen, March 15 2016 Newtonian Gravity Free-falling frames: Galilean symmetries Earth-based
More informationThe TT Deformation of Quantum Field Theory
The TT Deformation of Quantum Field Theory John Cardy University of California, Berkeley All Souls College, Oxford ICMP, Montreal, July 2018 Introduction all QFTs that we use in physics are in some sense
More informationCollective Effects. Equilibrium and Nonequilibrium Physics
Collective Effects in Equilibrium and Nonequilibrium Physics: Lecture 4, April 7, 2006 1 Collective Effects in Equilibrium and Nonequilibrium Physics Website: http://cncs.bnu.edu.cn/mccross/course/ Caltech
More informationStatus of viscous hydrodynamic code development
Status of viscous hydrodynamic code development Yuriy KARPENKO Transport group meeting, Jan 17, 2013 Yuriy Karpenko (FIAS/BITP) Status of viscous hydro code Transport group meeting, Jan 17, 2013 1 / 21
More informationHolographic matter at finite chemical potential
Holographic matter at finite chemical potential Talk at NumHol 2016 Santiago de Compostela, Spain Aristomenis Donos Durham University Base on work with: J. P. Gauntlett, E. Banks, T. Griffin, L. Melgar,
More informationTowards the shear viscosity of a cold unitary fermi gas
Towards the shear viscosity of a cold unitary fermi gas Jiunn-Wei Chen National Taiwan U. Shear viscosity y V x (y) x Frictional force T ij iv j ( x) V 2 j i ( x) 1 ij V ( x). 3 Shear viscosity measures
More informationFluid Equations for Rarefied Gases
1 Fluid Equations for Rarefied Gases Jean-Luc Thiffeault Department of Applied Physics and Applied Mathematics Columbia University http://plasma.ap.columbia.edu/~jeanluc 21 May 2001 with E. A. Spiegel
More informationFluid Equations for Rarefied Gases
1 Fluid Equations for Rarefied Gases Jean-Luc Thiffeault Department of Applied Physics and Applied Mathematics Columbia University http://plasma.ap.columbia.edu/~jeanluc 23 March 2001 with E. A. Spiegel
More informationLinear transport and hydrodynamic fluctuations
Linear transport and hydrodynamic fluctuations Pavel Kovtun University of Victoria Vienna, August 25, 2010 Pavel Kovtun (University of Victoria) Linear transport and hydro fluctuations Vienna, August 25,
More informationEnergy-momentum tensor correlators in hot Yang-Mills theory
Energy-momentum tensor correlators in hot Yang-Mills theory Aleksi Vuorinen University of Helsinki Micro-workshop on analytic properties of thermal correlators University of Oxford, 6.3.017 Mikko Laine,
More informationConstraints on Fluid Dynamics From Equilibrium Partition Func
Constraints on Fluid Dynamics From Equilibrium Partition Function Nabamita Banerjee Nikhef, Amsterdam LPTENS, Paris 1203.3544, 1206.6499 J. Bhattacharya, S. Jain, S. Bhattacharyya, S. Minwalla, T. Sharma,
More informationDynamic Density and Spin Responses in the BCS-BEC Crossover: Toward a Theory beyond RPA
Dynamic Density and Spin Responses in the BCS-BEC Crossover: Toward a Theory beyond RPA Lianyi He ( 何联毅 ) Department of Physics, Tsinghua University 2016 Hangzhou Workshop on Quantum Degenerate Fermi Gases,
More informationShock waves in the unitary Fermi gas
Shock waves in the unitary Fermi gas Luca Salasnich Dipartimento di Fisica e Astronomia Galileo Galilei, Università di Padova Banff, May 205 Collaboration with: Francesco Ancilotto and Flavio Toigo Summary.
More informationUniversal features of Lifshitz Green's functions from holography
Universal features of Lifshitz Green's functions from holography Gino Knodel University of Michigan October 19, 2015 C. Keeler, G.K., J.T. Liu, and K. Sun; arxiv:1505.07830. C. Keeler, G.K., and J.T. Liu;
More informationarxiv: v1 [nucl-th] 18 Apr 2019
Prepared for submission to JHEP Emergence of hydrodynamical behavior in expanding quark-gluon plasmas arxiv:1904.08677v1 [nucl-th] 18 Apr 2019 Jean-Paul Blaizot a and Li Yan b a Institut de Physique Théorique,
More informationNon-Equilibrium Steady States Beyond Integrability
Non-Equilibrium Steady States Beyond Integrability Joe Bhaseen TSCM Group King s College London Beyond Integrability: The Mathematics and Physics of Integrability and its Breaking in Low-Dimensional Strongly
More informationAn Introduction to AdS/CFT Correspondence
An Introduction to AdS/CFT Correspondence Dam Thanh Son Institute for Nuclear Theory, University of Washington An Introduction to AdS/CFT Correspondence p.1/32 Plan of of this talk AdS/CFT correspondence
More informationAnisotropic Interior Solutions in Hořava Gravity and Einstein-Æther Theory
Anisotropic Interior Solutions in and Einstein-Æther Theory CENTRA, Instituto Superior Técnico based on DV and S. Carloni, arxiv:1706.06608 [gr-qc] Gravity and Cosmology 2018 Yukawa Institute for Theoretical
More informationInsight into strong coupling
Thank you 2012 Insight into strong coupling Many faces of holography: Top-down studies (string/m-theory based) Bottom-up approaches pheno applications to QCD-like and condensed matter systems (e.g. Umut
More informationQuantum Fields in Curved Spacetime
Quantum Fields in Curved Spacetime Lecture 3 Finn Larsen Michigan Center for Theoretical Physics Yerevan, August 22, 2016. Recap AdS 3 is an instructive application of quantum fields in curved space. The
More information