Inhomogeneous thermalization and strongly coupled thermal flow via holography Daniel Fernández Max Planck Institute for Physics in Munich Iberian Strings 2016 - Madrid IFT

Time-dependent Holography Quark-gluon plasma thermalization [Chesler, Yaffe, Heller, Romatschke, Mateos, vd Schee, Bantilan] Turbulence in Gravity [Lehner, Green, Yang, Zimmerman, Chesler, Adams, Liu] Driven superconductors [Rangamani, Rozali, Wong] Quantum quenches [Balasubramanian, Buchel, Myers, van Niekerk, Das] Revivals [Mas, Lopez, Serantes, da Silva] 1 2 Collisions modeled as shockwaves Thermal flow modeled as dynamical horizon 1/14

Part 1: Heavy Ion Collisions

Hydrodynamics approach Conservation Law: Slow evolution of expectation values. Assumption: local quasi-equilibrium. Gradient expansion: Include viscosity term: 1st and higher order gradient terms In HICs, the kind of physics that dominates is viscous fluid dynamics. Connection to holography: Condition to work: small gradients. But good description of HIC data! [Luzum, Romatschke ‘09] 2/14

Evolution of a Heavy Ion Collision (Picture not to scale) Out of equilibrium Non-hydro degrees of freedom are dominant. Gravitational model: Shock wave collisions. Hydrodynamization Transition to the hydrodynamics approximation. Thermalization Isotropy of the diagonal components of Tmn in local rest frame. Hadronization Kinetic theory is applicable. 3/14

Gravitational formulation Ansatz: Boundary EOM: Generalize Simplification from 3+1 to 2+1 by: Alternative: Use polar coordinates. Assuming boost invariance and breaking rotational symmetry, 4/14

Initial Condition 5/14 Gaussian shocks Two separated shocks with finite thickness and energy density, moving toward each other: Exact analytic solution, in Fefferman-Graham coordinates. is the bdry. energy density, arbitrary if Choice: t r null geodesics AH EH Characteristic Formulation [Winicour ’01, Chesler, Yaffe ‘08] Ingoing Eddington-Finkelstein coordinates. Foliation of null hypersurfaces. IR cutoff → require fixed-r Apparent Horizon condition. (Generalize for perturbations) 5/14

Stress-Energy Tensor results Energy density: The inhomogeneities are evolved on top of the dynamical background: 6/14

Comparing with hydrodynamics Compare with hydro results Mid-rapidity Dramatic rise in the pressures. Very anisotropic and out-of-eq. Hydro holds almost from the beginning. [Chesler, Yaffe ‘10] Isotropization time and hydrodynamization time are completely different. [Fernández ’15] 7/14

Outlook: Chiral Magnetic Effect Strong magnetic fields are produced by the charged “spectators” ( ) Anomalous electric currents → Observable effects in hadron production. In a Heavy Ion Collision: In relativistic chiral plasma, the anomaly is present: → Anomalous electric current: Holomodel ingredients Massive → Emulate dynamical gluons for . Scalar field → Recover gauge invariance. CS term → Non-dynamical part of anomaly. [Rebhan, Schmitt, Stricker '09] [Gürsoy, Kharzeev, Rajagopal ’14] [Jiménez-Alba, Landsteiner, Melgar ‘15] Stückelberg-Chern-Simons theory: …evolution of axial charge? 8/14

Part 2: Thermal Flow

Universal regime of thermal transport [Bernard, Doyon ’12] Two exact copies initially at equilibrium, independently thermalized. Thermal quench in 1+1 Conservation eqs & tracelessness: NOPE Expectation for CFT: shock waves emanating from interface, converge to non-equilibrium Steady State. 9/14

Thermal transport in d>1 [Bhaseen, Doyon, Lucas, Schalm ’13] Generalization to any d Assume ctant. homogeneous heat flow as well: Effective dimension reduction to 1+1. Linear response regime: → Hydro eqs. explicitly solvable. Long time limit Final steady state characterized by Generic d prediction where 10/14

Hydrodynamics approach Heat transport dominated by diffusion instead of flow? Shockwave velocities: I III II Hydrodynamical evolution of 3 regions Match solutions ↔ Asymptotics of the central region with Two configurations: - Thermodynamic branch - “second branch” [Bhaseen, Doyon, Lucas, Schalm ’13] [Chang, Karch, Yarom ’13] 11/14

Holographic approach 12/14 [Amado, Yarom ’15] Energy transport: Lorentz-boosted thermal distribution → Expectation: Boosted black brane Gravitational problem: Full out-of-equilibrium evolution of Einstein’s equations. Ansatz: Energy density Energy flux 12/14

Information Flow How does information get exchanged between the systems which are isolated at t=0? Entanglement entropy → Holographic measure: Regularization: Substract result at T=0: y x z 13/14

Entanglement Entropies Ac B A Mutual Information What do we learn about A by looking at B? Shockwaves transport information. M.I. grows as shocks pass through the region. [Erdmenger, Fernández, Flory, Megías, Straub ’15] 14/14

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