Thermalization from gauge/gravity duality: Evolution of singularities in unequal time correlators

We consider a gauge/gravity dual model of thermalization which consists of a collapsing thin matter shell in asymptotically Anti-de Sitter space. A central aspect of our model is to consider a shell moving at finite velocity as determined by its equation of motion, rather than a quasi-static approximation as considered previously in the literature. By applying a divergence matching method, we obtain the evolution of singularities in the retarded unequal time correlator $G^R(t,t')$, which probes different stages of the thermalization. We find that the number of singularities decreases from a finite number to zero as the gauge theory thermalizes. This may be interpreted as a sign of decoherence. Moreover, in a second part of the paper, we show explicitly that the thermal correlator is characterized by the existence of singularities in the complex time plane. By studying a quasi-static state, we show the singularities at real times originate from contributions of normal modes. We also investigate the possibility of obtaining complex singularities from contributions of quasi-normal modes.Comment: 35 pages, 4 figure

Time singularities of correlators from Dirichlet conditions in AdS/CFT

Within AdS/CFT, we establish a general procedure for obtaining the leading singularity of two-point correlators involving operator insertions at different times. The procedure obtained is applied to operators dual to a scalar field which satisfies Dirichlet boundary conditions on an arbitrary time-like surface in the bulk. We determine how the Dirichlet boundary conditions influence the singularity structure of the field theory correlation functions. New singularities appear at boundary points connected by null geodesics bouncing between the Dirichlet surface and the boundary. We propose that their appearance can be interpreted as due to a non-local double trace deformation of the dual field theory, in which the two insertions of the operator are separated in time. The procedure developed in this paper provides a technical tool which may prove useful in view of describing holographic thermalization using gravitational collapse in AdS space.Comment: 30 pages, 3 figures. Version as in JHE

Holographic Evolution of Entanglement Entropy

We study the evolution of entanglement entropy in a 2-dimensional equilibration process that has a holographic description in terms of a Vaidya geometry. It models a unitary evolution in which the field theory starts in a pure state, its vacuum, and undergoes a perturbation that brings it far from equilibrium. The entanglement entropy in this set up provides a measurement of the quantum entanglement in the system. Using holographic techniques we recover the same result obtained before from the study of processes triggered by a sudden change in a parameter of the hamiltonian, known as quantum quenches. Namely, entanglement in 2-dimensional conformal field theories propagates with velocity v^2=1. Both in quantum quenches and in the Vaidya model equilibration is only achieved at the local level. Remarkably, the holographic derivation of this last fact requires information from behind the apparent horizon generated in the process of gravitational collapse described by the Vaidya geometry. In the early stages of the evolution the apparent horizon seems however to play no relevant role with regard to the entanglement entropy. We speculate on the possibility of deriving a thermalization time for occupation numbers from our analysis.Comment: 26 pages, 10 figure

Early-Time Energy Loss in a Strongly-Coupled SYM Plasma

We carry out an analytic study of the early-time motion of a quark in a strongly-coupled maximally-supersymmetric Yang-Mills plasma, using the AdS/CFT correspondence. Our approach extracts the first thermal effects as a small perturbation of the known quark dynamics in vacuum, using a double expansion that is valid for early times and for (moderately) ultrarelativistic quark velocities. The quark is found to lose energy at a rate that differs significantly from the previously derived stationary/late-time result: it scales like T^4 instead of T^2, and is associated with a friction coefficient that is not independent of the quark momentum. Under conditions representative of the quark-gluon plasma as obtained at RHIC, the early energy loss rate is a few times smaller than its late-time counterpart. Our analysis additionally leads to thermally-corrected expressions for the intrinsic energy and momentum of the quark, in which the previously discovered limiting velocity of the quark is found to appear naturally.Comment: 39 pages, no figures. v2: Minor corrections and clarifications. References added. Version to be published in JHE

On holographic thermalization and gravitational collapse of massless scalar fields

In this paper we study thermalization in a strongly coupled system via AdS/CFT. Initially, the energy is injected into the system by turning on a spatially homogenous scalar source coupled to a marginal composite operator. The thermalization process is studied by numerically solving Einstein's equations coupled to a massless scalar field in the Poincare patch of AdS_5. We define a thermalization time t_T on the AdS side, which has an interpretation in terms of a spacelike Wilson loop in CFT. Here T is the thermal equilibrium temperature. We study both cases with the source turned on in short(Delta t = 1/T) durations. In the former case, the thermalization time t_T = g_t/T <= 1/T and the coefficient g_t = 0.73 in the limit Delta t <= 0.02/T. In the latter case, we find double- and multiple-collapse solutions, which may be interpreted as the gravity duals of two- or multi-stage thermalization in CFT. In all the cases our results indicate that such a strongly coupled system thermalizes in a typical time scale t_T=O(1)/T.Comment: 25 papers, 13 figures, Minor modifications, details of numerics added, references added, final version to appear in JHE

From Navier-Stokes To Einstein

We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual geometry has an intrinsically flat timelike boundary segment $\Sigma_c$ whose extrinsic curvature is given by the stress tensor of the Navier-Stokes fluid. We consider a "near-horizon" limit in which $\Sigma_c$ becomes highly accelerated. The near-horizon expansion in gravity is shown to be mathematically equivalent to the hydrodynamic expansion in fluid dynamics, and the Einstein equation reduces to the incompressible Navier-Stokes equation. For $p=2$, we show that the full dual geometry is algebraically special Petrov type II. The construction is a mathematically precise realization of suggestions of a holographic duality relating fluids and horizons which began with the membrane paradigm in the 70's and resurfaced recently in studies of the AdS/CFT correspondence.Comment: 15 pages, 2 figures, typos correcte

Thermodynamics and Instabilities of a Strongly Coupled Anisotropic Plasma

We extend our analysis of a IIB supergravity solution dual to a spatially anisotropic finite-temperature N=4 super Yang-Mills plasma. The solution is static, possesses an anisotropic horizon, and is completely regular. The full geometry can be viewed as a renormalization group flow from an AdS geometry in the ultraviolet to a Lifshitz-like geometry in the infrared. The anisotropy can be equivalently understood as resulting from a position-dependent theta-term or from a non-zero number density of dissolved D7-branes. The holographic stress tensor is conserved and anisotropic. The presence of a conformal anomaly plays an important role in the thermodynamics. The phase diagram exhibits homogeneous and inhomogeneous (i.e. mixed) phases. In some regions the homogeneous phase displays instabilities reminiscent of those of weakly coupled plasmas. We comment on similarities with QCD at finite baryon density and with the phenomenon of cavitation.Comment: 62 pages, 13 figures; v2: typos fixed, added reference

Adherence to colorectal cancer screening guidelines in Canada

<p>Abstract</p> <p>Background</p> <p>To identify correlates of adherence to colorectal cancer (CRC) screening guidelines in average-risk Canadians.</p> <p>Methods</p> <p>2003 Canadian Community Health Survey Cycle 2.1 respondents who were at least 50 years old, without past or present CRC and living in Ontario, Newfoundland, Saskatchewan, and British Columbia were included. Outcomes, defined according to current CRC screening guidelines, included adherence to: i) fecal occult blood test (FOBT) (in prior 2 years), ii) endoscopy (colonoscopy/sigmoidoscopy) (prior 10 years), and iii) adherence to CRC screening guidelines, defined as either (i) or (ii). Generalized estimating equations regression was employed to identify correlates of the study outcomes.</p> <p>Results</p> <p>Of the 17,498 respondents, 70% were non-adherent CRC screening to guidelines. Specifically, 85% and 79% were non-adherent to FOBT and endoscopy, respectively. Correlates for all outcomes were: having a regular physician (OR = (i) 2.68; (ii) 1.91; (iii) 2.39), getting a flu shot (OR = (i) 1.59; (ii) 1.51; (iii) 1.55), and having a chronic condition (OR = (i) 1.32; (ii) 1.48; (iii) 1.43). Greater physical activity, higher consumption of fruits and vegetables and smoking cessation were each associated with at least 1 outcome. Self-perceived stress was modestly associated with increased odds of adherence to endoscopy and to CRC screening guidelines (OR = (ii) 1.07; (iii) 1.06, respectively).</p> <p>Conclusion</p> <p>Healthy lifestyle behaviors and factors that motivate people to seek health care were associated with adherence, implying that invitations for CRC screening should come from sources that are independent of physicians, such as the government, in order to reduce disparities in CRC screening.</p

Innate Immune Responses of Pulmonary Epithelial Cells to Burkholderia pseudomallei Infection

10.1371/journal.pone.0007308PLoS ONE410