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##### What is common for strongly coupled atoms and QGP?

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**``Two plasmas” workshop at RIKEN/BNL, Dec. 2004**What is common forstronglycoupled atomsand QGP? Edward Shuryak Department of Physics and Astronomy University at Stony Brook**Outline of the talk**• What can we learn ? • “Quantum viscosity” may be the smallest possible? • The role of pairing in both systems • (N=4 SUSY YM at strong coupling) has • Similar properties (not to be • Discussed) • =>A lesson: trasport properties are more instructive than EoS Motivations/background: • Why should one discuss trapped atoms here? • => a!1 means strongly coupled liquid • RHIC revolution => strongly coupled Quark-Gluon Plasma • Hydro works very well in both cases • => remarkably small viscosity observed**(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) -> molecules (BEC) • New spectroscopy in QCD at T>Tc, 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)? Shuryak at BNL, Dec.2004**Strongly coupled atoms**Shuryak at BNL, Dec.2004**What can a relation be, between cold fermionic atoms and**two-component plasmas? • Let us rename atoms: spin up=“+”, spin down=“-” • + and – attract => via Feshbach resonance, trying to form a Cooper pair/molecule • ++,-- repel each other => Via ``Pauli repulsion” as identical fermions Shuryak at BNL, Dec.2004**Smooth transition from fermi (BCS) to bose**(BEC)(A.Legett,1985) • The main variable x=1/apF X<<-1 Weakly attractive, molecular bound states Which at zero energy is Bose-condensed X>>1 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**``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 EoSE/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? Shuryak at BNL, Dec.2004**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 Shuryak at BNL, Dec.2004**The coolest thing on Earth, T=10 nK or 10^(-12) eV can**actually produce a Micro-Bang ! Elliptic flow with ultracold trapped Li6 atoms, a=> 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 10^6 or so! Is it a good liquid? How good?**Viscosity: a naïve approach**AS a!1 this gets meaningless ``Unitarity limited” regime: <max=4/k2 is also naïve as we will see: the interaction is not a 2-body scattering at all Shuryak at BNL, Dec.2004**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 ….**What is the smallest viscosity possible?**agrees with Ads/CFT at !1 • For CFT • /~ s>1/4 • For cold atoms we estimated /~n>1/6 Sketch of the argument (Gelman, ES, Zahed,nucl-th/0410067): The Einstein formula relates to diffusion • ~/2 • 0 classically**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**Applying hydrodynamics**• Hydrostatic equilibrium gives the shape for given EoS • Standard theory of small oscillations • Viscosity is treated perturbatively (Gelman,ES, Zahed):**The r-mode: conflicting results**The curves: hydro with the same EoS, Agrees with Duke results but not Insbrook one, some ocasional resonance? Shuryak at BNL, Dec.2004**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!**RHIC produced ``matter”, not a fireworks of partons !**• 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. • Viscosityis 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 What it means? (the micro scale) << (the macro scale) (the mean free path) << (system size) (relaxation time) << (evolution duration) I**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**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 =>/~ s ¼ 1/10 Nearly ideal hydro !? D.Teaney(’03)**Very large cross sections are needed to reproduce the**magnitude of v2! Huge cross sections!! Shuryak at BNL, Dec.2004**Pairing of quasiparticles in QGP**• Marginal states right in the RHIC domain (ES+Zahed,2003) • Lattice evidences: charmonium and light quark mesons (Hatsuda…) • New picture of EoS: a mixture of quasiparticles with bound pairs, including colored ones (ES+Zahed, 2004) Shuryak at BNL, Dec.2004**New QCD Phase Diagram, which includes ``zero binding**lines” at which can be large! (ES+I.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**Asakawa-Hatsuda, T=1.4Tc**Karsch-Laerman, T=1.5 and 3 Tc Shuryak at BNL, Dec.2004**Fitting F to screened Coulomb**• Fit from Bielefld group hep-lat/0406036 • Note that the Debye radius corresponds to``normal” (still enhanced by factor 2) coupling, while the overall strength of the potential is much larger Shuryak at BNL, Dec.2004**How many bound states at T>Tc?ES+I.Zahed, hep-ph/0403127**• In QGP there is no confinement => Hundreds of colored channels have bound states as well! Shuryak at BNL, Dec.2004**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! Shuryak at BNL, Dec.2004**(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 N=4 SUSY YM, where it is parametric, exp(-1/2) for large ´ g2NcÀ 1) Shuryak at BNL, Dec.2004**The pressure puzzle is resolved(ES and I.Zahed, 2004)**Shuryak at BNL, Dec.2004**Can we verify it experimentally?Dileptons from sQGP: at**1.7 and at about 2 GeV? Casalderrey+ES,hep-ph Shuryak at BNL, Dec.2004**QGP:**EoS is p/pideal gas¼ .8 at T>2Tc QGP seems to be near-perfect fluid /~ s » .1 » 1/(4) Conclusions: • Cold atoms: • pressure¼.5 at resonance • trapped atoms in a strong coupling • regime is a very good liquid as well! • /~ n» .5§ .3**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! Shuryak at BNL, Dec.2004**Resonance enhancement near zero binding lines: Explanation**for large cross section? (ES+Zahed,03)**If a Coulomb coupling is too strong,falling onto the center**may occur:but it is impossible to get a bindingcomparable to the massBut we need massless pion/sigma at T=>Tc • 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 T>Tc • Their contribution is » |(0)|2 which is calculated from strong Coulomb problem**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**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 T=Tc. • Both are not yet the potentials! • The lower figure shows the effective coupling constant