What is common for strongly coupled atoms and QGP?

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What is common forstrongly coupled atomsand QGP?
Two plasmas workshop at RIKEN/BNL, Dec. 2004

• Edward Shuryak
• Department of Physics and Astronomy
• University at Stony Brook

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Outline of the talk

• What can we learn ?
• Quantum viscosity
• may be the smallest possible?
• The role of pairing
• in both systems
• (N4 SUSY YM at strong coupling) has
• Similar properties (not to be
• Discussed)
• gtA lesson trasport properties are more
  instructive than EoS

• Motivations/background
• Why should one discuss trapped atoms here?
• gt a! 1 means strongly coupled liquid
• RHIC revolution gt strongly coupled Quark-Gluon
  Plasma
• Hydro works very well in both cases
• gt remarkably small viscosity observed

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(Outline continued)

• Lattice Effective masses are large
• m 3 T
• Spectroscopy in CFT, T? 0 has similar but
  parametric puzzles
• The bound states contribute to p(T) nearly as
  much as quasiparticles

• Another lesson the pairing into marginal states
  does it
• Cooper pairs (BCS) -gt molecules (BEC)
• New spectroscopy in QCD at TgtTc, Multiple bound
  states, 90 of them colored. (If so, it explains
  several puzzles related to lattice results) Large
  scattering lengths near zero binding lines, right
  at RHIC (T 1.5-2 Tc)?

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Strongly coupled atoms
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What can a relation be, between cold fermionic
atoms and two-component plasmas?

• Let us rename atoms
• spin up, spin down-
• and attract gt via Feshbach resonance, trying
  to form a Cooper pair/molecule
• ,-- repel each other gt
• Via Pauli repulsion as identical fermions

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Smooth transition from fermi (BCS) to bose
(BEC)(A.Legett,1985)

• The main variable x1/apF

Xltlt-1 Weakly attractive, molecular bound
states Which at zero energy is Bose-condensed
Xgtgt1 Fermi side, Attraction only near fermi
surface BCS and Cooper pairs
X close to 0 The Feshbach Resonance, Here we
expect the strongly coupled liquid
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Universality at the resonance(basically, just
a dimensional analysis Heiselberg)

• As a! 1 it cannot appear in any answer, so we are
  left with m,n,
• For EoS E/N (1-b) (3/5)2 n2/3/m is the only
  choice and b¼ .5 at the resonance
• Naïve approach (Stoof) as position of the
  resonance moves down, Fermi sphere diminishes and
  vanishes at the resonance, so why ? is not 1?

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My quick theory of ?
Pauli repulsion due to path antisymmetrization
Even for ideal case, the node surface enclose a
fermion It is the same in molecular regime (b)
but now p2/2(2m) Leading to 1-?¼ 1/2
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The coolest thing on Earth, T10 nK or 10(-12)
eV can actually produce a Micro-Bang !
Elliptic flow with ultracold trapped Li6 atoms,
agt infinity regime via the so called Feshbach
resonance The system is extremely dilute, but it
still goes into a hydro regime, with an elliptic
flow cross section changes by about 106 or so!
Is it a good liquid? How good?
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Viscosity a naïve approach
AS a! 1 this gets meaningless Unitarity
limited regime ?lt?max4?/k2 is also naïve as
we will see the interaction is not a 2-body
scattering at all
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Viscosity and universality

• There is no need to specify constituents or a
  mean free path
• Hydro damping of sound waves can provide a
  definition

• For cold atoms quantum viscosity
• ?/ n??
• Should be the universal
• dimensionless constant
• Scattering rate must be ?-1 /?F .

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What is the smallest viscosity possible?
agrees with Ads/CFT at ?! 1

• For CFT
• ?/ sgt1/4?
• For cold atoms we estimated ?/ngt1/6?

Sketch of the argument (Gelman, ES,
Zahed,nucl-th/0410067) The Einstein formula
relates ? to diffusion

• /2
• 0 classically

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What is the actual viscosity for a strongly
coupled atomic liquid?

• But before we come to that, we need to be sure
  that hydrodynamics works
• Elliptic flow in principle provide a limit since
  it agrees with ideal hydro, ?0
• Small oscillations of the trap Kinast et al
  (Duke) and Berenstein et al (Insbrook)
• Very elongated trap, slow z-mode and more rapid
  r-mode

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Applying hydrodynamics

• Hydrostatic equilibrium gives the shape for given
  EoS
• Standard theory of small oscillations
• Viscosity is treated perturbatively (Gelman,ES,
  Zahed)

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The r-mode conflicting results
The curves hydro with the same EoS, Agrees with
Duke results but not Insbrook one, some ocasional
resonance?
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Hydro works for up to 1000 oscillations! The z
mode frequency agrees with hydro (red star) at
resonance, with universal EoS Viscosity has a
strong minimum there

• B.Gelman, ES,I.Zahed
• nucl-th/0410067
• ?/ n
• ¼ .5 .3 is reached at the experimental minimum.
• Is it indeed a quantum viscosity?
• About as perfect as sQGP!

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Quark-gluon plasma
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RHIC produced matter, not a fireworks of
partons !

• What it means?
• (the micro scale) ltlt (the macro scale)
• (the mean free path) ltlt (system size)
• (relaxation time) ltlt (evolution duration)
• I

• Good equilibration (including strangeness) is
  seen in particle rations (as at SPS)
• the zeroth order in l/L is called an ideal
  hydro with a local stress tensor.
• Viscosity is the first order O(l/L) effect,
  velocity gradients.
• Note ? m.f.p. 1/? is inversely proportional
  to ? and is thus (the oldest) strong coupling
  expansion tool

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Radial and Elliptic Flows for ?,K,N?,D
STAR, PRC66(02)034904
PHENIX, PRL91(03)182301.
Elliptic flow rapidly rises with energy Because
we have surpassed The softest point
and Entered the QGP with high p/? ratio!
See details in a review by P.Kolb and U.Heinz,
nucl-th/0305084
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Viscosity of QGP
(D.Teaney,2003)
QGP at RHIC seem to be the most ideal fluid
known, viscosity/entropy .1 or so water would
not flow if only a drop with 1000 molecules be
made

• viscous corrections

1st order correction to dist. fn.
Corr (?/s)pt2
?s Sound attenuation length
gt?/ s ¼ 1/10
Nearly ideal hydro !?
D.Teaney(03)
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Very large cross sections are needed to reproduce
the magnitude of v2!
Huge cross sections!!
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Pairing of quasiparticles in QGP

• Marginal states right in the RHIC domain
• (ESZahed,2003)
• Lattice evidences charmonium and light quark
  mesons (Hatsuda)
• New picture of EoS a mixture of quasiparticles
  with bound pairs, including
• colored ones (ESZahed, 2004)

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New QCD Phase Diagram, which includes zero
binding lines at which ? can be large!
(ESI.Zahed hep-ph/030726)
T
The lines marked RHIC and SPS show the paths
matter makes while cooling, in Brookhaven (USA)
and CERN (Switzerland)
Chemical potential ?B related to baryon charge
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Asakawa-Hatsuda, T1.4Tc
Karsch-Laerman, T1.5 and 3 Tc
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Fitting F to screened Coulomb

• Fit from Bielefld group hep-lat/0406036

Note that the Debye radius corresponds
tonormal (still enhanced by factor 2)
coupling, while the overall strength of the
potential is much larger
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How many bound states at TgtTc?ESI.Zahed,
hep-ph/0403127

• In QGP there is no confinement gt Hundreds of
  colored channels have bound states as well!

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The pressure puzzle (GENERAL)

• Well known lattice prediction (numerical
  calculation, lattice QCD, Karsch et al) the
  pressure as a function of T (normalized to that
  for free quarks and gluons)
• This turned out to be the most misleading picture
  we had, fooling us for nearly 20 years
• p/p(SB).8 from about .3 GeV to very large value.
  Interpreted as an argument that interaction is
  relatively weak (0.2) and can be resumed,
  although pQCD series are bad
• BUT we recently learned that storng coupling
  leads to about 0.8 as well!

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(The pressure puzzle, cont.)

• How quasiparticles, which according to direct
  lattice measurements are heavy (Mq,Mg 3T)
  (Karsch et al) can provide enough pressure?
  (exp(-3)1/20)
• (The same problems appears in N4 SUSY YM, where
  it is parametric, exp(-?1/2) for large ?
  g2NcÀ 1)

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The pressure puzzle is resolved(ES and I.Zahed,
2004)
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Can we verify it experimentally?Dileptons from
sQGP ? at 1.7 and ? at about 2 GeV?
CasalderreyES,hep-ph
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Conclusions

• Cold atoms
• pressure¼ .5 at resonance
• trapped atoms in a strong coupling
• regime is a very good liquid as well!
• ?/ n .5 .3

• QGP
• EoS is p/pideal gas ¼ .8 at Tgt2Tc
• QGP seems to be near-perfect fluid
• ?/ s .1 1/(4?)

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Conclusions (continue)

• Marginal states in both cases,
• In QGP at the endpoints of binary states
• New spectroscopy In sQGP many old mesons
  plus 300 of colored binary states. May lead to
  large scattering lengths
• In both cases we badly need a theory of
  viscosity!

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Additional slides
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Resonance enhancement near zero binding lines
Explanation for large cross section? (ESZahed,03)
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If a Coulomb coupling is too strong,falling onto
the center may occurbut it is impossible to get
a bindingcomparable to the massBut we need
massless pion/sigma at TgtTc

• Brown,Lee,Rho,ES hep-ph/0312175 near-local
  interaction induced by the instanton molecules
  
• (also called hard glue or epoxy, as they
  survive
• at TgtTc
• Their contribution is ?(0)2 which is
  calculated from strong Coulomb problem

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New potentials (cont)after the entropy term is
subtracted,potentials become much deeper
this is how potential I got look like for T 1
1.2 1.4 2 4 6 10Tc, from right to left, from
ES,Zahed hep-ph/0403127
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New free energies for static quarks (from
Bielfeld)

• Upper figure is normalized at small distances
  one can see that there is large effective mass
  for a static quark at TTc.
• Both are not yet the potentials!
• The lower figure shows the effective coupling
  constant

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Here is the binding and psi(0)2