what is common for strongly coupled atoms and qgp? edward shuryak department of physics and...

What is common forWhat is common forstronglystrongly coupled atomscoupled atomsand and QGP?QGP?

Edward ShuryakEdward ShuryakDepartment of Physics and Department of Physics and

AstronomyAstronomy

University at Stony Brook University at Stony Brook

``Two plasmas” workshop at RIKEN/BNL, Dec. 2004

Shuryak at BNL, Dec.2004

Outline of the talkOutline of the talkMotivations/Motivations/

background:background: Why should one Why should one

discuss trapped discuss trapped atoms here? atoms here?

=> => aa!! 11 means means strongly coupled strongly coupled liquidliquid

RHIC revolution => RHIC revolution => strongly coupled strongly coupled Quark-Gluon PlasmaQuark-Gluon Plasma

Hydro works very Hydro works very well in both caseswell in both cases

=> remarkably small => remarkably small viscosity observedviscosity observed

•What can we learn ? What can we learn ? How small viscosityHow small viscositymay be?may be?The role of pairingThe role of pairingIn both systemsIn both systems•(N=4 SUSY YM at (N=4 SUSY YM at strong coupling) hasstrong coupling) hasSimilar properties (not to beSimilar properties (not to beDiscussed)Discussed)

=>A lesson: =>A lesson: trasport trasport properties are properties are more more instructive than instructive than EoSEoS


(Outline (Outline continued)continued)

Another lesson: the Another lesson: the pairing mechanism into pairing mechanism into marginal statesmarginal states are are importantimportant

Cooper pairs (BCS) -> Cooper pairs (BCS) -> molecules (BEC)molecules (BEC)

New spectroscopy in QCD New spectroscopy in QCD at T>Tcat T>Tc, , Multiple bound Multiple bound states, 90% of them states, 90% of them colored. (If so, it explains colored. (If so, it explains several puzzles related to several puzzles related to lattice results) Large lattice results) Large scattering lengths near scattering lengths near zero binding lineszero binding lines, (T= , (T= 1.5-2 Tc)?1.5-2 Tc)?

Spectroscopy in CFT, T 0 solves similar puzzles

•Effective mass

•Potentials from ladders good even for relativistic states, for

exchanges v/c» 1/4 >>1

•The bound states are much lighter than quasiparticles


Strongly coupled atomsStrongly coupled atoms


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


Smooth transition from fermi (BCS) to bose (BEC)

(A.Legett,1985)

• The main variable x=1/apF

X>>1Fermi side,Attraction only near fermi surfaceBCS and Cooper pairs

X close to 0The Feshbach Resonance,Here we expect thestrongly coupled liquid

X<<-1Weakly attractive, molecular bound statesWhich at zero energy isBose-condensed


``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= (3/5)~2 n2/3/m is the only choice and ¼ .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?


My quick theory of Pauli repulsion due to path antisymmetrization

Even for ideal case, the node surface enclose a fermionIt is the same in molecular regime (b) but now p2/2(2m)Leading to 1-¼ 1/2

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?

The coolest thing on Earth, T=10 nK or 10^(-12) eV can actually produce a

Micro-Bang !


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


Viscosity and universality

• There is no need to specify constituents or idea of a mean free path:

• Hydro: damping of sound waves can provide a definition

•For cold atoms • / ~ n=

Should be the universal dimensionless constant•Scattering rate must be -1» ~/F ….


What is the smallest viscosity possible?

• For CFT /~ s>1/4• For cold atoms

/~n>1/6

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

~/20 classically

agrees with Ads/CFT at ! 1

What is the actual viscosity What is the actual viscosity for a strongly coupled for a strongly coupled atomic liquid?atomic liquid?• But before we come to that, we need to But before we come to that, we need to

be sure that be sure that hydrodynamics workshydrodynamics works

• Elliptic flow in principle provide a limit Elliptic flow in principle provide a limit since it agrees with since it agrees with ideal hydro, ideal hydro, =0=0

• Small oscillations of the trap: Kinast et al Small oscillations of the trap: Kinast et al (Duke) and Berenstein et al (Insbrook):(Duke) and Berenstein et al (Insbrook):

• Very elongated trap, Very elongated trap, slow z-modeslow z-mode and and more rapid r-modemore rapid r-mode

Applying hydrodynamicsApplying hydrodynamics

• Hydrostatic Hydrostatic equilibrium gives equilibrium gives the shape for given the shape for given EoSEoS

• Standard theory of Standard theory of small oscillationssmall oscillations

• Viscosity is treated Viscosity is treated perturbativelyperturbatively (Gelman,ES, Zahed):(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?

Hydro works for up to 1000 oscillations! Hydro works for up to 1000 oscillations! The z mode frequency agrees with hydro The z mode frequency agrees with hydro (red star)(red star) at resonance, with universal at resonance, with universal EoS EoS Viscosity has a strong Viscosity has a strong minimum thereminimum there

B.Gelman, ES,I.Zahed nucl-th/0410067

~ n¼ .5§ .3 is reached at the experimental minimum.

About as perfect as sQGP!

Quark-gluon plasmaQuark-gluon plasma

RHIC produced ``matter”,RHIC produced ``matter”, not a fireworks of partons not a fireworks of partons ! !

What it means?What it means?(the micro scale) << (the macro scale)(the micro scale) << (the macro scale)

(the mean free path) << (system size)(the mean free path) << (system size)(relaxation time) << (evolution duration) (relaxation time) << (evolution duration)

II•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

Radial and Elliptic Flows Radial and Elliptic Flows for for ,K,N…,K,N…,D …,D …

See details in a review by P.Kolb and U.Heinz, nucl-th/0305084

STAR, PRC66(’02)034904PHENIX, PRL91(’03)182301.

Elliptic flow rapidly rises with energyBecause we have surpassed``The softest point” andEntered the QGP with highp/ ratio!

Viscosity of QGPViscosity of QGPQGP at RHIC seem to be the most idealfluid known, viscosity/entropy =.1 or so water would not flow if only a drop with 1000 molecules be made

• viscous corrections1st order correction to dist. fn.:

s :Sound attenuation length

Nearly ideal hydro !? D.Teaney(’03)

=>/~ s ¼ 1/10

(D.Teaney,2003)

Corr» (/s)pt2


Very large cross sections are needed to reproduce the magnitude of v2!

Huge cross sections!!


Pairing of quasiparticles in QGP

• Marginal states right in the RHIC domain

(ES+Zahed,2003)

• Lattice evidences: charmonium and light quark mesons

• New picture of EoS: a mixture of quasiparticles with bound pairs, including

colored ones (ES+Zahed, 2004)

New QCD New QCD Phase Phase Diagram, Diagram, which which includes includes ``zero binding ``zero binding lines” at lines” at which which can can be large! be large! (ES+I.Zahed (ES+I.Zahed hep-ph/03072hep-ph/030726)6)

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


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


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!


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!


(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)


The pressure puzzle is resolved(ES and I.Zahed, 2004)


Can we verify it experimentally?Dileptons from sQGP: at 1.7 and

at about 2 GeV? Casalderrey+ES,hep-ph


Conclusions:

QGP:

• EoS is p/pideal gas ¼ .8 at T>2Tc

• QGP seems to be near-perfect fluid

/~ s » .1 » 1/(4)

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!

Additional slidesAdditional slides

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

If a Coulomb coupling is too strong,If a Coulomb coupling is too strong,falling onto the center may occur:falling onto the center may occur:but it is impossible to get a bindingbut it is impossible to get a bindingcomparable to the masscomparable to the massBut we need massless pion/sigma at But we need massless pion/sigma at T=>TcT=>Tc• Brown,Lee,Rho,ES hep-Brown,Lee,Rho,ES hep-

ph/0312175 : near-local ph/0312175 : near-local interaction induced by interaction induced by the the `ìnstanton `ìnstanton molecules”molecules”

(also called ``hard glue” or (also called ``hard glue” or `èpoxy”, as they `èpoxy”, as they survive survive

at T>Tat T>Tcc

• Their contribution is Their contribution is »» | |(0)|(0)|22 which is calculated which is calculated from strong Coulomb from strong Coulomb problemproblem

New potentials (cont):New potentials (cont):after the entropy term is subtracted,after the entropy term is subtracted,potentials become potentials become much deepermuch 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 New ``free energies” for static quarks (from Bielfeld)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

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

what is common for strongly coupled atoms and qgp? edward shuryak department of physics and...

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