Stochastic Variational Method for Viscous Hydrodynamics

Abstract

In this short review, we focus on some of the subjects, related to J. Cleymans’ pioneering contribution of statistical approaches to the particle production process in heavy-ion collisions. We discuss these perspectives from the effects of stochastic processes in collective variables of hydrodynamic description, which is described by a stochastic variational method. In this connection, we stress also the necessity of the inclusion of surface and quantum effects in the study of relativistic heavy-ion reactions.

Possible enhancements of collective flow anisotropy induced by uncertainty relation for fluid element

“…We have focused on the effect of the velocity fluctuation in the simple freeze-out process. There are many fluctuation effects which are not considered in the present toy model: kinematic and statistical fluctuations around freeze-out [1,3,28], fluctuation in collective behaviors over many collisional events (EbE fluctuation) [4,12,29], and stochastic behaviors appearing in hydrodynamical evolutions itself [30,31]. In this paper, we considered the physics related to the relativistic heavy-ion collisions.…”

“…In this section, we briefly summarize the properties of the stochastic motion of the fluid element in the NSF equation, following the review papers [8,12,13].…”

“…The first term on the right-hand side is the additional term which does not appear in the NSF equation. This term is important to discuss the surface effect and quantum fluctuation [8,11,12,[16][17][18]. In the present work, however, we simply ignore this term by setting α B = 0, leading to κ = 0.…”

Study of the medium effects in jet observables in relativistic heavy-ion collisions

“…However, there is a need for more realistic medium simulations, which is fulfilled by the state-of-the-art v-USPhydro code [11,12]. This code utilizes the Smooth Particle Hydrodynamics (SPH) Lagrangian method [13,14] to solve the viscous hydrodynamic equations of the QGP in the transverse plane on an event-by-event basis, considering different initial conditions and incorporating transverse and viscosity expansion, which are absent in the original model.…”