The hydrodynamic model and its applications

Abstract

As an effective description of the underlying theory at the long-wavelength limit, hydrodynamics plays a crucial role in various sections of Science. In relativistic heavy-ion collisions, the quark-gluon plasma can be reasonably modeled by a strongly coupled fluid with small viscosity. Meanwhile, however, the apparent success also leads to further speculations as well as challenges on the theoretical side. In this regard, the anti-de Sitter/conformal field theory correspondence provides an intriguing possibility to study a strongly interacting field theory via a counterpart, which is a weakly interacting classical theory of gravity. On the experimental side, the beam energy scan program has been initiated at the relativistic heavy-ion collider at Brookhaven national laboratory. It might provide essential information on the highly nonlinear system, and in particular, those associated with transport properties, collectivity, and phase transition. The present proposal constitutes a continuation of the research project (FAPESP no. 2014/06354-1) on the hydrodynamical model and some of its pertinent applications. Our main focus is the hydrodynamic approach for the relativistic heavy-ion collisions and the fluid/gravity duality. We plan to investigate the properties of the hydrodynamical model for relativistic heavy-ion collisions, and particularly, those related to the critical phenomenon. The studies will be carried out by employing the numerical approach, such as the SPheRIO code, while focused on the simulations associated with the ongoing experiments. Among others, we plan to work on topics related to multiplicity fluctuations, particle correlations, and chiral hydrodynamical models. On the other hand, we also propose to explore the physical system in the framework of the Einstein-Maxwell-dilaton theory through the fluid/gravity duality. The latter will be performed regarding a better understanding of the concepts related to the Green function, such as critical exponents, quasinormal modes, and pole skipping. (AU)