Nearly perfect liquids: strongly coupled systems from quark-gluon plasmas to ultracold atoms Gordon...
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![Page 1: Nearly perfect liquids: strongly coupled systems from quark-gluon plasmas to ultracold atoms Gordon Baym University of Illinois 8 April 2009 8 April 2009.](https://reader035.fdocuments.in/reader035/viewer/2022070413/5697bfca1a28abf838ca97bf/html5/thumbnails/1.jpg)
Nearly perfect liquids: Nearly perfect liquids: strongly coupled systems strongly coupled systems
from quark-gluon plasmas to from quark-gluon plasmas to ultracold atomsultracold atoms
Gordon BaymGordon Baym
University of IllinoisUniversity of Illinois
8 April 20098 April 2009
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Deconfined quark-gluon plasmas
made in ultrarelativistic heavy ion collisions
T ~ 102 MeV ~ 1012 K (temperature of early universe at ~1 sec)
Trapped cold atomic systems: Bose-condensed and BCS fermion superfluid states T ~ nanokelvin (traps are the coldest places in the universe!)
Separated by ~21 decades in characteristic energy scales -- intriguing overlaps.
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Small clouds with many degrees of freedom ~ 104 – 107
Strongly interacting systems
Finite size systems w. edge problems (trap edge, hadronic halo)
Infrared miseries in qcd and condensed bosons.
Viscosity: heavy-ion elliptic flow Fermi gases near unitarity
Ultracold ionized atomic plasma physics
Crossover: BEC BCS and hadron quark-gluon plasma
Connections:
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Cold atoms as testing ground for qcd:
Bose-fermion mixtures => RG diquarks + B quarks
3 Fermi systems => simulate formation of baryons from 3 quarks
Non-Abelian atomic systems => simulate lattice gauge theory with atoms in optical lattices.
Superfluidity and pairing in unbalanced systems: trapped fermions color superconductivity
Test relativistic plasma codes in ultracold atom dynamics (hydro to collisionless)
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Both systems scale-free in strongly coupled regime
In cold atoms near resonance only length-scale is density. No microscopic parameters enter equation of state:
is a universal parameter. No systematic expansion
Theory: = -0.60 (0.2) Green’s Function Monte Carlo, Gezerlis & Carlson (2008)
Experiment: -0.61(2) Duke (2008)
Fqgp ~ const nexc4/3 Ecold atoms ~ const n2/3/m
( => CFT)
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Strongly coupled systems
In quark-gluon plasma,
Even at GUT scale, 1015GeV, gs ~ 1/2 (cf. electrodynamics: e2/4 = 1/137 => e~ 1/3)
QGP is always strongly interacting
In cold atoms, effective atom-atom interaction is short range and s-wave: a = s-wave atom-atom scattering length. Cross section: =8 a2
Go from weakly repulsive to strongly repulsive to strongly attractive to weakly attractive by dialing external magnetic field through Feshbach resonance .
6Li
~ 150 MeV
repulsive
attractive
Resonance at B= 830 G
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Remarkably similar behavior of ultracold fermionic atoms
and low density neutron matter (ann= -18.5 fm)
A. Gezerlis and J. Carlson, Phys. Rev. C 77, 032801(R) (2008)A. Gezerlis and J. Carlson, Phys. Rev. C 77, 032801(R) (2008)
nn effectiverange beginsto play role
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Strong coupling leads to low first viscosity seen in expansion in both systems
= scattering time
Viscosity in elliptic flow in heavy ion collisions and in Fermi gases near unitarity
First viscosity
Strong interactions => small
Shear viscosity Shear viscosity ::
F = F = A v /d A v /ddd vv
Stress tensorStress tensor
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Conjectured lower bound on ratio of first viscosity to entropy density, s: Kovtun, Son, & Starinets, PRL 94 (2005)
~ n~ ntt m v m v22 = n p = n p , s ~ n, s ~ ntt
nntt = no. of degrees of freedom producing viscosity = no. of degrees of freedom producing viscosity
p = mv = mean particle momentum ~ p = mv = mean particle momentum ~ / (interparticle spacing) / (interparticle spacing) = mean free path= mean free path
Bound Bound mean free path > interparticle spacing mean free path > interparticle spacing
Equality exact in N=4supersymmetric Yang Mills theoryin limit of large number of colors, Nc: AdS/CFT duality
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Familiar (weakly interacting) systems well obey bound
Degenerate Fermi gas:
Classical gas: nmv2hard spheres), s ~ log T /slog T , growing with T
, s ~ T (Fermi liquid) /s , dropping with T
Low T Bose gas: : s ~ Ts ~ T3 3 (phonons) (phonons)
/s ~ 1/T/s ~ 1/T88, dropping with T, dropping with T
Have minimum (at T ~ TF in the absence of other scales)
In He-II, /s ~0.7~ at minimum (T ~ 2K)
cf. unitary Fermi gas, /s ~0.2~ at minimum (T ~ 0.2 TF)
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Laurence Yaffe – QCD transport theory
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Shear viscosity/ entropy density ratio vs. T/TShear viscosity/ entropy density ratio vs. T/TFF
TTcc
Shear viscosity from radial breathing modeShear viscosity from radial breathing mode
Data:J. Thomas et al.
Theory: T. Schaefer, Phys. Rev. A 76, 063618 (2007)
G. Rupak & T .Schaefer, PRA76, 053607 (2007)
G.M.Bruun &H. Smith, PRA75, 043612 (2007)
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Expt: Expt: A. Turlapov, J. Kinast, B. Clancy, L. Luo, J. Joseph, and J.E. Thomas, J. Low Temp. Phys. (2007)
Ratio of shear viscosity to entropy density (in units of ) Ratio of shear viscosity to entropy density (in units of )
Shear viscosity of Fermi gas at unitarityShear viscosity of Fermi gas at unitarity
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Hydrodynamic predictions of v2(pT)
Elliptic flow => almost vanishing viscosity in quark-gluon plasmaElliptic flow => almost vanishing viscosity in quark-gluon plasma
M. Luzum & P. Romatschke, 0804.4015
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Derek Teaney -- Viscosity in v2 and RAA v2 and RAA
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Viscosity issues:
In heavy ion collisions:
How to extract viscosity from heavy ion collisions?
Validity of hydro? Dependence on pt?
Higher order terms in gradients? Second viscosity effects?
Edge of collision volume: mfp ~ gradients
In cold atoms:
Transport: Boltzmann eqn with medium effects at unitarity?
Effective range corrections – away from unitarity
Breakdown of strong interactions as denity -> 0 at edge of trap
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Dam Son
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Chris Herzog
BEC transition
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John McGreevy: Non-relativistic CFT – applications to cold atoms
not unitary fermions (yet)
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BEC-BCS crossover in Fermi systemsBEC-BCS crossover in Fermi systems
Continuously transform from molecules to Cooper pairs: D.M. Eagles (1969) A.J. Leggett, J. Phys. (Paris) C7, 19 (1980) P. Nozières and S. Schmitt-Rink, J. Low Temp Phys. 59, 195 (1985)
Tc/Tf ~ 0.2 Tc /Tf ~ e-1/kfa
Pairs shrink
6Li
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(color superconductivity)
QGP (quark-gluon plasma)
Phase diagram of quark-gluon plasmaT. Hatsuda
Chiral symmetry breaking chirally symmetric (Bose-Einstein decondensation)
CROSSOVER ??
Neutrons, protons, pions, … paired quarks
(density)
tricritical point
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Interplay between BCS pairing and chiral condensate Interplay between BCS pairing and chiral condensate
Hadronic phase breaks chiral symmetry, producing chiral (particle-Hadronic phase breaks chiral symmetry, producing chiral (particle-antiparticle) bosonic condensate: antiparticle) bosonic condensate:
Color superconducting phase has particle-particle pairing Color superconducting phase has particle-particle pairing
~~ 33
b
~ d~ dLL** d dRR
Spontaneous breaking of the axial U(1)Spontaneous breaking of the axial U(1)AA symmetry of QCD (axial symmetry of QCD (axial
anomaly) leads to attractive (‘t Hooft anomaly) leads to attractive (‘t Hooft 6-quark6-quark interaction) between interaction) between the chiral condensate and pairing fields. Each encourages the other! the chiral condensate and pairing fields. Each encourages the other!
a,b,c = colori,j,k = flavorC: charge conjugation
ddRR
ddLL**
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Hatsuda, Tachibana, Yamamoto & GB, PRL 97, 122001 (2006); PRD 76, 074001 (2007)
New critical point in phase diagram: induced by chiral condensate – diquark pairing coupling
via axial anomaly
Hadronic
Normal
Color SC
(as ms increases)
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Phase diagram of cold fermionsvs. interaction strength
(magnetic field B)
Unitary regime (Feshbach resonance) -- crossoverNo phase transition through crossover
BCS
BEC of di-fermionmolecules
Temperature
Tc
Free fermions +di-fermion molecules
Free fermions
-1/kf a0
a>0a<0
Tc/EF ~0.22
Tc~ EFe-/2kF|a|
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Atomic Bose-Fermi mixtures: model diquark-quark to baryon transition
GB, K. Maeda, T. Hatsuda, in preparation
KRb
RbK
Binding of 40K + 87RbPhases vs gbf (<0)
weak gbb>0
strong gbb>0
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Ken O’Hara – Ultracold three component Fermi gas
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Cheng Chin – Superfluid – Mott insulator transition in Cs in optical lattices
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Simulating U(2) non-Abelian gauge theory
D. Jaksch and P. Zoller, New J. Phys. 5, 56 (2003)
-arXiv:0902.3228
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Michael Murillo – Strongly coupled plasmas
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Strongly coupled plasmas: = Einteraction /Ekinetic >> 1
Electrons in a metal
Eint ~ e2/r0 r0 = interparticle spacing ~ 1/kf
Eke ~ kf2/m => ~ e2/ vf = eff
vf ~ 10-2-10-3c => eff ~ 1-5
Dusty interstellar plasmas
Laser-induced plasmas (NIF, GSI)
Quark-gluon plasmas
Eint ~ g2/r0, r0 ~ 1/T, Eke ~ T => ~ g2 > 1
Ultracold trapped atomic plasmas
Non-degenerate plasma, Eke~ T => = Eint/Eke ~ e2/r0T
~ n91/3/TK [where n9 = n/(109 /cm3) and T
K = (T/ 1K)]
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Ultracold plasmas analog systems for gaining understanding of plasma properties relevant to heavy-ion collisions:
-kinetic energy distributions of electrons and ions -modes of plasmas: plasma oscillations -screening in plasmas-nature of expansion – flow, hydrodynamical (?)-thermalization times-correlations-interaction with fast particles-viscosity-...
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Quark-gluon plasma
Hadronic matter2SC
CFL
1 GeV
150 MeV
0
Temp
eratur
e
Baryon chemical potential
Neutron stars
?
Ultrarelativistic heavy-ion collisions
Nuclear liquid-gas
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Superfluidity and pairing for unbalanced systems
Trapped atoms: change relative populations of two states by hand
QGP: balance of strange (s) quarks to light (u,d) depends on
ratio of strange quark mass ms to chemical potential (>0)
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Phase diagram of trapped imbalanced Fermi gases
Trap geometryTrap geometry
superfluid core
normal normal envelopeenvelope
MIT
Shin, Schnuck, Schirotzek, & Ketterle, Nature 451, 689 (2008)