Hydro+: hydrodynamics with parametric slowing down and fluctuations near the critical point

The search for the QCD critical point in heavy-ion collision experiments requires dynamical simulations of the bulk evolution of QCD matter as well as of fluctuations. We consider two essential ingredients of such a simulation: a generic extension of hydrodynamics by a_parametrically_ slow mode or modes ("Hydro+") and a description of fluctuations out of equilibrium. By combining the two ingredients we are able to describe the bulk evolution and the fluctutations within the same framework. Critical slowing down means that equilibration of fluctuations could be as slow as hydrodynamic evolution and thus fluctuations could significantly deviate from equilibrium near the critical point. We generalize hydrodynamics to partial-equilibrium conditions where the state of the system is characterized by the off-equilibrium magnitude of fluctuations in addition to the usual hydrodynamic variables -- conserved densities. We find that the key element of the new formalism -- the extended entropy taking into account the off-equilibrium fluctuations -- is remarkably similar to the 2PI action in quantum field theory. We show how the new Hydro+ formalism reproduces two major effects of critical fluctuations on the bulk evolution: the strong frequency dependence of the anomalously large bulk viscosity as well as the stiffening of the equation of state with increasing frequency or wave-number. While the agreement with known results confirms its validity, the fact that Hydro+ achieves this within a local and deterministic framework gives it significant advantages for dynamical simulations.Comment: 46 pages, 5 figure

Charmonium moving through a strongly coupled QCD plasma: a holographic perspective

We study the properties of charmonium in a strongly coupled QCD-like plasma at finite momentum. As a basis for this study, a "bottom-up" holographic model is used which has been previously shown to reproduce charmonium phenomenology in vacuum and give a reasonable dissociation temperature at zero momentum. The finite momentum spectral functions are presented and found to be consistent with recent lattice results. The in-medium dispersion relation and momentum dependence of decay width of J/Psi have also been studied. We find no signature of a subluminal limiting velocity from the dispersion relation, while we note that the dissociation temperature decreases with momentum faster than previous holographic models. Based upon the dissociation temperature, a maximum momentum for J/Psi in medium is identified and its phenomenological implications on J/Psi suppression are discussed.Comment: 23 pages, 8 figures. References added. Published versio

A self-organising mixture network for density modelling

A completely unsupervised mixture distribution network, namely the self-organising mixture network, is proposed for learning arbitrary density functions. The algorithm minimises the Kullback-Leibler information by means of stochastic approximation methods. The density functions are modelled as mixtures of parametric distributions such as Gaussian and Cauchy. The first layer of the network is similar to the Kohonen's self-organising map (SOM), but with the parameters of the class conditional densities as the learning weights. The winning mechanism is based on maximum posterior probability, and the updating of weights can be limited to a small neighbourhood around the winner. The second layer accumulates the responses of these local nodes, weighted by the learning mixing parameters. The network possesses simple structure and computation, yet yields fast and robust convergence. Experimental results are also presente