Hydrodynamic fluctuations of entropy in one-dimensionally expanding system

The fluctuation-dissipation relation tells that dissipation always accompanies with thermal fluctuations. Relativistic fluctuating hydrodynamics is used to study the effects of the thermal fluctuations in the hydrodynamic expansion of the quark-gluon plasma created in the high-energy nuclear collisions. We show that the thermal noise obeys the steady-state fluctuation theorem when (i) the time scales of the evolution of thermodynamic quantities are sufficiently longer than the relaxation time, and (ii) the thermal fluctuations of temperature are sufficiently small. The steady-state fluctuation theorem describes the distribution of the entropy which can be related to the multiplicity observed in high-energy nuclear collisions. As a consequence, we propose an upper bound to the multiplicity fluctuations which is useful to test the initial state models. We also numerically investigate breaking of the steady-state fluctuation theorem due to the non-vanishing relaxation time in real nuclear collisions.

Dynamically integrated transport approach for heavy-ion collisions at high baryon density

We develop a new dynamical model for high energy heavy-ion collisions in the beam energy region of the highest net-baryon densities on the basis of non-equilibrium microscopic transport model JAM and macroscopic 3+1D hydrodynamics by utilizing a dynamical initialization method. In this model,dynamical fluidization of a system is controlled by the source terms of the hydrodynamic fields. In addition, time dependent core-corona separation of hot regions is implemented. We show that our new model describes multiplicities and mean transverse mass in heavy-ion collisions within a beam energy region of $3<sqrt{s_{NN}}<30$ GeV. Good agreement of the beam energy dependence of the $K^+/pi^+$ ratio is obtained, which is explained by the fact that a part of the system is not thermalized in our core-corona approach.

Hydrodynamic fluctuations and dissipation in an integrated dynamical model

We develop a new integrated dynamical model to investigate the effects of the hydrodynamic fluctuations on observables in high-energy nuclear collisions. We implement hydrodynamic fluctuations in a fully 3-D dynamical model consisting of the hydrodynamic initialization models of the Monte-Carlo Kharzeev-Levin-Nardi model, causal dissipative hydrodynamics and the subsequent hadronic cascades. By analyzing the hadron distributions obtained by massive event-by-event simulations with both of hydrodynamic fluctuations and initial-state fluctuations, we discuss the effects of hydrodynamic fluctuations on the flow harmonics, $v_n$ and their fluctuations.

Multiplicity fluctuation from hydrodynamic noise

We discuss multiplicity fluctuation caused by noises during hydrodynamic evolution of the quark-gluon fluid created in high-energy nuclear collisions.

Theory Summary

In this review, I show a personal overview of theoretical results shown in the International Conference on the Initial Stages in High-Energy Nuclear Collision, in Illa da Toxa, Galicia, Spain, Sept.~8-14, 2013.

Relativistic fluctuating hydrodynamics with memory functions and colored noises

Relativistic dissipative hydrodynamics including hydrodynamic fluctuations is formulated by putting an emphasis on non-linearity and causality. As a consequence of causality, dissipative currents become dynamical variables and noises appeared in an integral form of constitutive equations should be colored ones from fluctuation-dissipation relations. Nevertheless noises turn out to be white ones in its differential form when noises are assumed to be Gaussian. The obtained ifferential equations are very useful in numerical implementation of relativistic fluctuating hydrodynamics.

Integrated Dynamical Approach to Relativistic Heavy Ion Collisions

We review integrated dynamical approaches to describe heavy ion reaction as a whole at ultrarelativistic energies. Since final observables result from all the history of the reaction, it is important to describe all the stages of the reaction to obtain the properties of the quark gluon plasma from experimental data. As an example of these approaches, we develop an integrated dynamical model, which is composed of a fully (3+1) dimensional ideal hydrodynamic model with the state-of-the-art equation of state based on lattice QCD, and subsequent hadronic cascade in the late stage. Initial conditions are obtained employing Monte Car

Dynamical modeling of high energy heavy ion collisions

We present theoretical approaches to high energy nuclear collisions in detail putting a special emphasis on technical aspects of numerical simulations. Models include relativistic hydrodynamics, Monte-Carlo implementation of k_T-factorization formula, jet quenching in expanding fluids, a hadronic transport model and the Vlasov equation for colored particles.

Elliptic flow in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV: hybrid model assessment of the first data

We analyze the elliptic flow parameter v_2 in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV and in Au+Au collisions at sqrt{s_{NN}} =200 GeV using a hybrid model in which the evolution of the quark gluon plasma is described by ideal hydrodynamics with a state-of-the-art lattice QCD equation of state, and the subsequent hadronic stage by a hadron cascade model. For initial conditions, we employ Monte-Car

Elliptic flow in U+U collisions at sqrt{s_{NN}} = 200 GeV and in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV: Prediction from a hybrid approach

We predict the elliptic flow parameter v_2 in U+U collisions at sqrt{s_{NN}}=200 GeV and in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV using a hybrid model in which the evolution of the quark gluon plasma is described by ideal hydrodynamics with a state-of-the-art lattice QCD equation of state, and the subsequent hadronic stage by a hadron cascade model.