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“Understanding confinement”, May 16-21, 2005 Quantum Black Holes, Strong Fields, and Relativistic Heavy Ions D. Kharzeev Outline • Black holes and accelerating observers • Event horizons and pair creation in strong fields • Thermalization and phase transitions in relativistic nuclear collisions DK, K. Tuchin, hep-ph/0501234 Black holes radiate S.Hawking ‘74 Black holes emit thermal radiation with temperature acceleration of gravity at the surface Similar things happen in non-inertial frames Einstein’s Equivalence Principle: Gravity Acceleration in a non-inertial frame An observer moving with an acceleration a detects a thermal radiation with temperature W.Unruh ‘76 In both cases the radiation is due to the presence of event horizon Black hole: the interior is hidden from an outside observer; Schwarzschild metric Accelerated frame: part of space-time is hidden (causally disconnected) from an accelerating observer; Rindler metric From pure to mixed states: the event horizons mixed state pure state mixed state pure state Thermal radiation can be understood as a consequence of tunneling through the event horizon Let us start with relativistic classical mechanics: velocity of a particle moving with an acceleration a classical action: it has an imaginary part… well, now we need some quantum mechanics, too: The rate of tunneling under the potential barrier: This is a Boltzmann factor with Accelerating detector • Positive frequency Green’s function (m=0): • Along an inertial trajectory • Along a uniformly accelerated trajectory x y 0,z (t 2 a2 )1/ 2 Unruh,76 detector is effectively immersed into a heat bath Accelerated at temperature TU=a/2 An example: electric field The force: The acceleration: The rate: What is this? Schwinger formula for the rate of pair production; an exact non-perturbative QED result factor of 2: contribution from the field The Schwinger formula eE e+ Dirac sea + + +… The Schwinger formula • Consider motion of a charged particle in a constant electric field E. Action is given by Equations of motion yield the trajectory where a=eE/m is the acceleration QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. Classically forbidden trajectory t it E • Action along the classical trajectory: m eE S(t) arcsh(at) 2 at( 1 a2t 2 2) arcsh(at) a 2a • In Quantum Mechanics S(t) is an analytical function of t m eE m 2 • Classically forbidden paths contribute to ImS(t) 2 a 2a 2eE • Vacuum decays with probability V m 1 exp e 2 Im S e 2 Im S m 2 / eE e Sauter,31 Weisskopf,36 Schwinger,51 • Note, this expression can not be expanded in powers of the coupling - non-perturbative QED! Pair production by a pulse Consider a time dependent field E A 0,0,0, tanh( k0 t) k0 E • Constant field limit k0 0 • Short pulse limit k0 spectrum with a thermal t Chromo-electric field: Wong equations • Classical motion of a particle in the external nonAbelian field: gfx Ý gFIÝq Ý IxÝaA mxÝ a abc I 0 b c The constant chromo-electric field is described by A0a Ez a3, Ai a 0 vector I3 precesses about 3-axis with I3=const Solution: 0 Ý Ý Ý Ý Ý Ý Ý x y 0,mz gEx I3 Effective Lagrangian: Brown, Duff, 75; Batalin, Matinian,Savvidy,77 An accelerated observer consider an observer with internal degrees of freedom; for energy levels E1 and E2 the ratio of occupancy factors Bell, Leinaas: depolarization in accelerators? For the excitations with transverse momentum pT: but this is all purely academic (?) Can one study the Hawking radiation on Earth? Gravity? Take g = 9.8 m/s2; the temperature is only Quic kTime™ and a TIFF (Unc ompres sed) dec ompres sor are needed to see this pic ture. Electric fields? Lasers? compilation by A.Ringwald Condensed matter black holes? “slow light”? Unruh ‘81; e.g. T. Vachaspati, cond-mat/0404480 Strong interactions? Consider a dissociation of a high energy hadron of mass m into a final hadronic state of mass M; The probability of transition: m M Transition amplitude: In dual resonance model: Unitarity: P(mM)=const, b=1/2 universal slope Hagedorn temperature! limiting acceleration Fermi - Landau statistical model of multi-particle production Hadron production at high energies is driven by statistical mechanics; universal temperature Enrico Fermi 1901-1954 Lev D. Landau 1908-1968 Where on Earth can one achieve the largest acceleration (deceleration) ? Relativistic heavy ion collisions! stronger color fields: Strong color fields (Color Glass Condensate) as a necessary condition for the formation of Quark-Gluon Plasma The critical acceleration (or the Hagedorn temperature) can be exceeded only if the density of partonic states changes accordingly; this means that the average transverse momentum of partons should grow CGC QGP Quantum thermal radiation at RHIC The event horizon emerges due to the fast decceleration of the colliding nuclei in strong color fields; Tunneling through the event horizon leads to the thermal spectrum Rindler and Minkowski spaces The emerging picture Big question: How does the produced matter thermalize so fast? Perturbation theory + Kinetic equations Fast thermalization horizons QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. collision point Qs Rindler coordinates: Gluons tunneling through the event horizons have thermal distribution. They get on mass-shell in t=2Qs (period of Euclidean motion) Deceleration-induced phase transitions? • Consider Nambu-Jona-Lasinio model in Rindler space L i (x) (x) 2N 2 2 ( ( x) (x)) ( ( x)i (x)) 5 • Commutation relations: (x), (x) 2g (x) • Rindler space: x t , 2 2 2 1 2 ln tx tx ds2 2d2 d 2 dx 2 e.g., Ohsaku ’04 Gap equation in an accelerated frame • Introduce the scalar and pseudo-scalar fields (x) ( x)(x) N (x) ( x)i 5(x) N • Effective action (at large N): Seff 2 2 d x g iln det(i i 5 ) 2 4 • Gap equation: 2i a d 2k sinh( /a) 2 2 d (K ( /a)) (K ( /a)) ) i / a 1/ 2 i / a1/ 2 2 2 (2 ) where 2 k 2 2 Rapid deceleration induces phase transitions QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. NambuJona-Lasinio model (BCS - type) Similar to phenomena in the vicinity of a large black hole: Rindler space Schwarzschild metric A link between General Relativity and QCD? solution to some of the RHIC puzzles? Black holes RHIC collisions