Nearly perfect liquids:

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Nearly perfect liquids strongly coupled
systems from quark-gluon plasmas to ultracold
atoms Gordon Baym University of Illinois
8 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 1m 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 gt RG diquarks B quarks
• 3 Fermi systems gt simulate formation of baryons
  from 3 quarks
• Non-Abelian atomic systems gt 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
( gt CFT)
Fqgp const nexc4/3 Ecold atoms
const n2/3/m
In cold atoms near resonance only length-scale is
density. No microscopic parameters enter
equation of state
b is a universal parameter. No systematic
expansion
Theory ? -0.60 (0.2) Greens Function Monte
Carlo, Gezerlis Carlson (2008) Experiment
-0.61(2) Duke (2008)
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Strongly coupled systems
In quark-gluon plasma,
L 150 MeV
Even at GUT scale, 1015GeV, gs 1/2 (cf.
electrodynamics e2/4p 1/137 gt 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 s8p a2 Go from weakly repulsive to
strongly repulsive to strongly attractive to
weakly attractive by dialing external magnetic
field through Feshbach resonance .

repulsive
6Li
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)?
nn effective range begins to play role
A. Gezerlis and J. Carlson, Phys. Rev. C 77,
032801(R) (2008)?
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Viscosity in elliptic flow in heavy ion
collisions and in Fermi gases near unitarity
Strong coupling leads to low first viscosity
h, seen in expansion in both systems
Shear viscosity ? F ? A v /d
v
d
Stress tensor
First viscosity
t scattering time
Strong interactions gt small h
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Conjectured lower bound on ratio of first
viscosity to entropy density, s
Kovtun, Son, Starinets, PRL 94 (2005)
Equality exact in N4 supersymmetric Yang Mills
theory in limit of large number of colors, Nc
AdS/CFT duality

• nt m v2? n p ?, s nt
• nt no. of degrees of freedom producing
  viscosity
• p mv mean particle momentum /
  (interparticle spacing)
• ? mean free path
• Bound ? mean free path gt interparticle spacing

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Familiar (weakly interacting) systems well obey
bound
Classical gas

• nmv2 ? T1/2 (hard spheres), s log T
• /s T1/2 /log T , growing with T

Degenerate Fermi gas

• 1/T2 , s T (Fermi liquid)
• /s 1/T3, dropping with T

Low T Bose gas ? 1/T5, s T3 (phonons)
?/s
1/T8, 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 from radial breathing mode
Theory T. Schaefer, Phys. Rev. A 76, 063618
(2007)
Tc
G. Rupak T .Schaefer, PRA76, 053607 (2007)
G.M.Bruun H. Smith, PRA 75, 043612 (2007)
Data J. Thomas et al.
Shear viscosity/ entropy density ratio vs. T/TF
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Shear viscosity of Fermi gas at unitarity
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 )
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Hydrodynamic predictions of v2(pT)
Elliptic flow gt 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 -gt
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 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)
Pairs shrink
6Li
Tc/Tf 0.2 Tc /Tf
e-1/kfa
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Phase diagram of quark-gluon plasma
T. Hatsuda
tricritical point
QGP (quark-gluon plasma)
chirally symmetric (Bose-Einstein decondensation)
Chiral symmetry breaking
Neutrons, protons, pions,
paired quarks
(color superconductivity)
CROSSOVER ??
(density)
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Interplay between BCS pairing and chiral
condensate
Hadronic phase breaks chiral symmetry, producing
chiral (particle-antiparticle) bosonic
condensate
Color superconducting phase
has particle-particle pairing
a,b,c color i,j,k flavor C charge conjugation
b
Spontaneous breaking of the axial U(1)A symmetry
of QCD (axial anomaly) leads to attractive (t
Hooft 6-quark interaction) between the chiral
condensate and pairing fields. Each encourages
the other!
dR
?
?
?
?3
dL dR?
?
dL
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New critical point in phase diagram induced
by chiral condensate diquark pairing
coupling via axial anomaly
Hatsuda, Tachibana, Yamamoto GB, PRL 97, 122001
(2006) PRD 76, 074001 (2007)
(as ms increases)?
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Phase diagram of cold fermionsvs. interaction
strength
(magnetic field B)?
Unitary regime (Feshbach resonance) --
crossover No phase transition through crossover
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Atomic Bose-Fermi mixtures model
diquark-quark to baryon transition
GB, K. Maeda, T. Hatsuda, in preparation
weak gbbgt0
strong gbbgt0
Binding of 40K 87Rb
Phases vs gbf (lt0)
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Ken OHara 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)
-arXiv0902.3228
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Michael Murillo Strongly coupled plasmas
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Strongly coupled plasmas G Einteraction
/Ekinetic gtgt 1 Electrons in a metal Eint
e2/r0 r0 interparticle spacing 1/kf
Eke kf2/m gt G e2/ vf aeff vf
10-2-10-3c gt aeff 1-5 Dusty interstellar
plasmas Laser-induced plasmas (NIF,
GSI) Quark-gluon plasmas Eint g2/r0, r0
1/T, Eke T gt G g2 gt 1 Ultracold trapped
atomic plasmas Non-degenerate plasma, Eke
T gt G Eint/Eke e2/r0T
G n91/3/TK where n9 n/(109
/cm3) and TK (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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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 ?
(gt0)?
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Phase diagram of trapped imbalanced Fermi gases
Shin, Schnuck, Schirotzek, Ketterle, Nature
451, 689 (2008)
MIT