A Vaidya type geometry describing gravitation collapse in asymptotically Lifshitz spacetime with hyperscaling violation provides a simple holographic model for thermalization near a quantum critical point with non-trivial dynamic and hyperscaling violation exponents. The allowed parameter regions are constrained by requiring that the matter energy momentum tensor satisfies the null energy condition. We present a combination of analytic and numerical results on the time evolution of holographic entanglement entropy in such backgrounds for different shaped boundary regions and study various scaling regimes, generalizing previous work by Liu and Suh.

The sudden injection of energy in a strongly coupled conformal field theory and its subsequent thermalization can be holographically modeled by a shell falling into anti-de Sitter space and forming a black brane. For a homogeneous shell, Bhattacharyya and Minwalla were able to study this process analytically using a weak field approximation. Motivated by event-by-event fluctuations in heavy ion collisions, we include inhomogeneities in this model, obtaining analytic results in a long wavelength expansion. In the early-time window in which our approximations can be trusted, the resulting evolution matches well Open Access doi:10.1007/JHEP10 (2013)082 JHEP10 (2013)082 with that of a simple free streaming model. Near the end of this time window, we find that the stress tensor approaches that of second-order viscous hydrodynamics. We comment on possible lessons for heavy ion phenomenology.

To describe theoretically the creation and evolution of the quark-gluon plasma, one typically employs three ingredients: a model for the initial state, non-hydrodynamic early time evolution, and hydrodynamics. In this paper we study the non-hydrodynamic early time evolution using the AdS/CFT correspondence in the presence of inhomogeneities. We find that the AdS description of the early time evolution is well-matched by free streaming. Near the end of the early time interval where our analytic computations are reliable, the stress tensor agrees with the second order hydrodynamic stress tensor computed from the local energy density and fluid velocity. Our techniques may also be useful for the study of far-from-equilibrium strongly coupled systems in other areas of physics.Strongly coupled quantum liquids are studied in many experimental settings: (a) quark-gluon matter created in ultrarelativistic heavy ion collisions, (b) strongly correlated electrons in metals, cuprates and heavy-fermion materials, and (c) condensates of ultra-cold atoms. The holographic AdS/CFT or gauge-gravity framework has provided new insights into the dynamics of such fluids. One development is the fluid/gravity correspondence [1] where one can derive hydrodynamic equations from Einstein's equations in a particular long wavelength limit, and even get complete second order hydrodynamic equations [2, 3] for conformal relativistic fluids. Another interesting question is how and when a far-from-equilibrium initial state approaches a regime where hydrodynamics becomes a good approximation. This article studies this question in an analytically tractable model that exhibits inhomogeneities.Experiments at RHIC and at the LHC have shown that already at very early times, at most 1 fm/c, the matter produced in heavy ion collisions shows collective behavior in agreement with viscous hydrodynamics. The argument about the presence of hydrodynamic behavior of the quark-gluon plasma created in heavy ion collisions rests primarily on two observations. First, one observes a cos(2φ) correlation between the azimuthal momentum direction of produced hadrons and the collision plane, which is known as "elliptic" flow, see [4][5][6][7] and references therein. This phenomenon can also be deduced from the azimuthal two-particle correlations among emitted hadrons, and is sometimes referred to as the "ridge" or "double-ridge" effect in studies in Pb+Pb collisions at the LHC [7][8][9][10].The second observation is related to event-by-event fluctuations [11,12]. Experimentally it was found for central heavy ion collisions that odd Fourier coefficients of the flow are not much smaller than even ones [7,8,13]. By a symmetry argument, odd coefficients can only be generated by fluctuations, so one is forced to conclude that fluctuations have large amplitudes. The parton saturation model for the initial nuclear state suggests also that the fluctuations are of short range in the plane transverse to the beam axis (of order of the inverse saturation scale 1/Q s ∼ 0.2 fm [14]). ...