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  1. ``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

  2. 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

  3. (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

  4. Strongly coupled atoms Shuryak at BNL, Dec.2004

  5. 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

  6. Shuryak at BNL, Dec.2004

  7. Shuryak at BNL, Dec.2004

  8. 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

  9. ``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

  10. 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

  11. 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?

  12. 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

  13. 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 ….

  14. 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

  15. 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

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

  17. 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

  18. 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!

  19. Quark-gluon plasma

  20. 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

  21. 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

  22. 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)

  23. Very large cross sections are needed to reproduce the magnitude of v2! Huge cross sections!! Shuryak at BNL, Dec.2004

  24. 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

  25. 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

  26. Asakawa-Hatsuda, T=1.4Tc Karsch-Laerman, T=1.5 and 3 Tc Shuryak at BNL, Dec.2004

  27. 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

  28. 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

  29. 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

  30. (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

  31. The pressure puzzle is resolved(ES and I.Zahed, 2004) Shuryak at BNL, Dec.2004

  32. 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

  33. 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

  34. 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

  35. Additional slides

  36. Shuryak at BNL, Dec.2004

  37. Shuryak at BNL, Dec.2004

  38. Shuryak at BNL, Dec.2004

  39. Shuryak at BNL, Dec.2004

  40. Resonance enhancement near zero binding lines: Explanation for large cross section? (ES+Zahed,03)

  41. 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

  42. 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

  43. 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

  44. Here is the binding and |psi(0)|^2