Asymptotic perfect fluid dynamics as a consequence of AdS/CFT

We study the dynamics of strongly interacting gauge-theory matter (modelling quark-gluon plasma) in a boost-invariant setting using the AdS/CFT correspondence. Using Fefferman-Graham coordinates and with the help of holographic renormalization, we show that perfect fluid hydrodynamics emerges at large times as the unique nonsingular asymptotic solution of the nonlinear Einstein equations in the bulk. The gravity dual can be interpreted as a black hole moving off in the fifth dimension. Asymptotic solutions different from perfect fluid behaviour can be ruled out by the appearance of curvature singularities in the dual bulk geometry. Subasymptotic deviations from perfect fluid behaviour remain possible within the same framework.Comment: 19 pages, 1 figure; v2: free streaming example changed to s=1; conclusions unchange

A numerical relativity approach to the initial value problem in asymptotically Anti-de Sitter spacetime for plasma thermalization - an ADM formulation

This article studies a numerical relativity approach to the initial value problem in Anti-de Sitter spacetime relevant for dual non-equilibrium evolution of strongly coupled non-Abelian plasma undergoing Bjorken expansion. In order to use initial conditions for the metric obtained in arXiv:0906.4423 we introduce new, ADM formalism-based scheme for numerical integration of Einstein's equations with negative cosmological constant. The key novel element of this approach is the choice of lapse function vanishing at fixed radial position, enabling, if needed, efficient horizon excision. Various physical aspects of the gauge theory thermalization process in this setup have been outlined in our companion article arXiv:1103.3452. In this work we focus on the gravitational side of the problem and present full technical details of our setup. We discuss in particular the ADM formalism, the explicit form of initial states, the boundary conditions for the metric on the inner and outer edges of the simulation domain, the relation between boundary and bulk notions of time, the procedure to extract the gauge theory energy-momentum tensor and non-equilibrium apparent horizon entropy, as well as the choice of point for freezing the lapse. Finally, we comment on various features of the initial profiles we consider.Comment: 25 pages, 9 figures, 1 table; see also the companion article arXiv:1103.3452; v2: typos fixed; v3: references added and updated, publishe

Viscous hydrodynamics relaxation time from AdS/CFT

We consider an expanding boost-invariant plasma at strong coupling using the AdS/CFT correspondence for N=4 SYM. We determine the relaxation time in second order viscous hydrodynamics and find that it is around thirty times shorter than weak coupling expectations. We find that the nonsingularity of the dual geometry in the string frame necessitates turning on the dilaton which leads to a nonvanishing expectation value for tr F^2 behaving like tau^(-10/3).Comment: 10 pages, Mathematica script included in the source; v2: typo in (28) fixed, statement about electric/magnetic modes correcte

Multiplying unitary random matrices - universality and spectral properties

In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a hamiltonian random in time. We find that the result is universal and depends only on the second moment of the generator of the stochastic evolution. We find indications of critical behavior (eigenvalue spacing scaling like $1/N^{3/4}$) close to $\theta=\pi$ for a specific critical evolution time $t_c$.Comment: 12 pages, 2 figure

Scaling Up Magnetic Nanobead Synthesis with Improved Stability for Biomedical Applications

The growing interest in multifunctional nano-objects based on polymers and magnetic nanoparticles for biomedical applications motivated us to develop a scale-up protocol to increase the yield of polymeric magnetic nanobeads while aiming at keeping the structural features at optimal conditions. The protocol was applied to two different types of magnetic ferrite nanoparticles: the Mn-ferrite selected for their properties as contrast agents in magnetic resonance imaging and iron oxide nanostar shaped nanoparticles chosen for their heat performance in magnetic hyperthermia. At the same time, some experiments on surface functionalization of nanobeads with amino modified polyethyelene glycol (PEG) molecules have provided further insight into the formation mechanism of magnetic nanobeads and the need to cross-link the polymer shell to improve the stability of the beads, making them more suitable for further manipulation and use. The present work summarizes the most important parameters required to be controlled for the upscaling of nanobead synthesis in a bench protocol and proposes an alternative cross-linking strategy based on prefunctionalization of the polymer prior to the nanobead formation as a key parameter to improve the nanobead structural stability in solutions at different pHs and during surface functionalization

Six and seven loop Konishi from Luscher corrections

In the present paper we derive six and seven loop formulas for the anomalous dimension of the Konishi operator in N=4 SYM from string theory using the technique of Luscher corrections. We derive analytically the integrand using the worldsheet S-matrix and evaluate the resulting integral and infinite sum using a combination of high precision numerical integration and asymptotic expansion. We use this high precision numerical result to fit the integer coefficients of zeta values in the final analytical answer. The presented six and seven loop results can be used as a cross-check with FiNLIE on the string theory side, or with direct gauge theory computations. The seven loop level is the theoretical limit of this Luscher approach as at eight loops double-wrapping corrections will appear.Comment: 18 pages, typos correcte

An fMRI study

Background Maternal sensitive behavior depends on recognizing one’s own child’s affective states. The present study investigated distinct and overlapping neural responses of mothers to sad and happy facial expressions of their own child (in comparison to facial expressions of an unfamiliar child). Methods We used functional MRI to measure dissociable and overlapping activation patterns in 27 healthy mothers in response to happy, neutral and sad facial expressions of their own school-aged child and a gender- and age- matched unfamiliar child. To investigate differential activation to sad compared to happy faces of one’s own child, we used interaction contrasts. During the scan, mothers had to indicate the affect of the presented face. After scanning, they were asked to rate the perceived emotional arousal and valence levels for each face using a 7-point Likert-scale (adapted SAM version). Results While viewing their own child’s sad faces, mothers showed activation in the amygdala and anterior cingulate cortex whereas happy facial expressions of the own child elicited activation in the hippocampus. Conjoint activation in response to one’s own child happy and sad expressions was found in the insula and the superior temporal gyrus. Conclusions Maternal brain activations differed depending on the child’s affective state. Sad faces of the own child activated areas commonly associated with a threat detection network, whereas happy faces activated reward related brain areas. Overlapping activation was found in empathy related networks. These distinct neural activation patterns might facilitate sensitive maternal behavior

Wishart and Anti-Wishart random matrices

We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices $A^\dagger A$, for any finite number of rows and columns of $A$, without any large N approximations. In particular we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure of reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks.Comment: 11 pages; v2: references updated + some clarifications added; v3: version to appear in J. Phys. A, Special Issue on Random Matrix Theor

Chiral Disorder in QCD

Using the Gell-Mann-Oakes-Renner (GOR) relation and semi-classical arguments, we show that the bulk quark spectrum in QCD exhibits a variety of regimes including the ergodic one described by random matrix theory. We analyze the quark spectral form-factor in the diffusive and ballistic regime. We suggest that a class of chiral transitions in QCD is possibly of the metal-insulator type, with a universal spectral statistics at the mobility edge

Correlation functions of three heavy operators - the AdS contribution

We consider operators in N=4 SYM theory which are dual, at strong coupling, to classical strings rotating in S^5. Three point correlation functions of such operators factorize into a universal contribution coming from the AdS part of the string sigma model and a state-dependent S^5 contribution. Consequently a similar factorization arises for the OPE coefficients. In this paper we evaluate the AdS universal factor of the OPE coefficients which is explicitly expressed just in terms of the anomalous dimensions of the three operators.Comment: 49 pages, 3 figures; v.2 references corrected; v3: corrected discussion in section 5, results unchange