collective effectsa basic feature distinguishing plasmas from ordinary matter simultaneous interaction of each charged particle with a considerable number of others due to long range of electromagnetic forces both charge-charge and charge-neutral interactions charge-neutral dominates in weakly ionized plasmas neutrals interact via distortion of e cloud by charges magnetic fields generated by moving charges give rise to magnetic interactions
Lecture 3 Properties of strongly coupled plasmas and what the string theorists tell us
1 Barbara Jacak Stony Brook University January 12, 2012 23,32,n2…
Outline
TODAY What’s a plasma? How we know QGP is strongly coupled Other strongly coupled systems Viscosity & Transport AdS/CFT correspondence and its application to strongly coupled systems Thermalization puzzle 2
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what is a plasma? 4th state of matter (after solid, liquid, gas) a plasma is: ionized gas, macroscopically neutral exhibits collective effects interactions among charges of multiple particles spreads charge into characteristic (Debye) length, lD multiple particles inside this length they screen each other plasma size > lD “normal” plasmas are electromagnetic (e + ions) quark-gluon plasma interacts via strong interaction
collective effects
a basic feature distinguishing plasmas from ordinary matter simultaneous interaction of each charged particle with a considerable number of others due to long range of electromagnetic forces both charge-charge and charge-neutral interactions charge-neutral dominates in weakly ionized plasmas neutrals interact via distortion of e cloud by charges magnetic fields generated by moving charges give rise to magnetic interactions
Plasma properties people investigate
moments of the distribution function of particles f(x,v) 0th moment → particle density (n) 1st moment → 2nd moment → pressure tensor, temperature 3rd moment → heat flux tensor Transport (e.g. diffusion, viscosity) hydrodynamic expansion velocity, shock propagation radiation bremsstrahlung, blackbody, collisional and recombination Screening Plasma oscillations, instabilities Wave propagation
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Debye screening in plasmas Debye length: distance over which the influence of an individual charged particle is felt by the other particles in the plasma charged particles arrange themselves so as to effectively shield any electrostatic fields within a distance of lD lD = e0kT ------- nee2 Debye sphere = sphere with radius lD Typically: # of electrons inside Debye sphere is large ND= N/VD= neVD VD= 4/3 p lD3 1/2 ne = number density e = charge
In Quark Gluon Plasma
lD = e0kT ------- nee2 kT is large! (> 170 MeV) Number density of color charges “ne” is also large But it is not a fixed density (gluon number is not fixed) It depends on kT! oh oh… Ask QCD, especially lattice QCD which is not perturbative i.e. need not assume coupling is weak, pairwise interactions 7 1/2
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Debye screening in QCD: a tricky concept in leading order QCD (O. Philipsen, hep-ph/0010327) vv
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don’t give up! ask lattice QCD running coupling coupling drops off for r > 0.3 fm Karsch, et al. Coupling between a pair of test quarks placed in system at temperature T/Tc
OK, let’s find the Debye length
r where coupling weakens must be related to lD Ask lattice QCD about this Think about the question in terms of masses: m~hc/L (since lattice cannot tell us length scales) What’s the mass of a gluon? Depends on the temperature In vacuum, gluon is massless In medium at temperature T, gluon mass is gT But also have color magnetic fields with gB ~ g4T2 -> magnetic gluons with mass g2T How to study screening mass on lattice? Calculate the gluon propagator* and see what happens to it as a function of T 10 * For experts – please see paper(s) in hep-lat on arXiv
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screening masses from gluon propagator Screening mass, mD, defines inverse length scale Inside this distance, an equilibrated plasma is sensitive to insertion of a static source Outside it’s not. T dependence of electric & magnetic screening masses Quenched lattice study of gluon propagator figure shows: mD,m= 3Tc, mD,e= 6Tc at 2Tc mD~hc/lD & hc=197 MeVfm lD ~ 0.4, 0.2 fm magnetic screening mass is non-zero not very gauge-dependent, but DOES grow w/ lattice size (long range is important) Nakamura, Saito & Sakai, hep-lat/0311024
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Implications of lD ~ 0.3 fm? can use to estimate plasma coupling parameter, G G = / but also given by G = 1/ND for lD = 0.3fm and e = 15 GeV/fm3 VD = 4/3 p lD3 = 0.113 fm3 ED = 1.7 GeV to convert ED to number of particles: use gT or g2T for T ~ 2Tc and g2 = 4 get ND = 1.2 – 2.5 G ~ 1 NB: for G ~ 1 plasma is NOT fully screened – strongly coupled! affects interaction s! strongly coupled EM plasmas behave as liquids, can even make crystals for G ≥ 150 dusty plasmas, cold atoms+ions , warm dense matter
AHA!
So, maybe we should have KNOWN the QGP will be strongly coupled! But we’d have to ask lattice QCD the right question We know of strongly coupled QGP from data: Near-perfect fluidity & low viscosity/entropy ratio Diffusion/short relaxation time of heavy quarks also yields small h/s Inability of pQCD to explain energy loss 13
14 Strong coupling: forefront issue in other fields! Quark gluon plasma is like other systems with strong coupling – all exhibit liquid properties & phase transitions Cold atoms: coldest & hottest matter on earth are alike! Dusty plasmas & warm, dense plasmas have liquid and even crystalline phases Strongly correlated condensed matter: liquid crystal phases and superconductors
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In all these cases have a competition Attractive forces repulsive force or kinetic energy In high Tc superconductors: magnetic vs. potential energy Result: many-body interactions, not pairwise! String theory and its duality with black holes ( coupling) provides tool to calculate dynamics of all these systems (see papers by Subir Sachdev, Sean Hartnoll, Chris Herzog and others for condensed matter applications)
Some examples
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Ultracold Li gas, use Feshbach resonance 10-7 K
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What they actually do Observe elliptic flow, as at RHIC!
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Set the gas rotating Get the viscosity from measured transport in the rotating gas F/A = h dvx/dz
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