Amaresh Jaiswal

Relativistic third-order dissipative fluid dynamics from kinetic theory

Fluid dynamics is an effective theory describing the long-wavelength limit of the microscopic dynamics of a system. While nonrelativistic fluid dynamics finds applications in various aspects of physics and engineering, the domain of applicability of relativistic fluid dynamics is in the field of astrophysics, cosmology and high-energy heavy-ion collisions. The collective behavior of the hot and dense matter (which is believed to have existed in the very early universe) created in ultra-relativistic heavy-ion collisions has been studied quite extensively within the framework of relativistic fluid dynamics. To study the evolution of a hydrodynamic system, it is natural to first employ the equations of ideal fluid dynamics. However, as ideal fluids are hypothetical by virtue of uncertainty principle [1], the dissipative effects can not be ignored. Relativistic dissipative fluid dynamics is formulated as an order-by-order expansion in gradients, ideal hydrodynamics being zeroth-order. The first-order theories, collectively known as relativistic Navier-Stokes (NS) theory, are due to Eckart [2] and Landau-Lifshitz [3]. However, these theories involve parabolic differential equations and suffer from acausality and numerical instability. The second-order theory by Israel and Stewart (IS) [4] with its hyperbolic equations solves the acausality problem [5] but may not guarantee stability. Despite the success of IS theory in explaining a wide range of collective phenomena observed in heavy-ion collisions, its formulation is based on strong assumptions and approximations. The original IS theory derived from Boltzmann equation (BE) uses two powerful assumptions in the derivation of dissipative equations: use of second moment of BE and the 14moment approximation [4, 6]. In Ref. [7], although the dissipative equations were derived directly from their definitions without resorting to second-moment of BE, however the 14-moment approximation was still employed. In Ref. [8] it was shown that both these assumptions are unnecessary and instead of 14-moment approximation, iterative solution of BE was used to obtain the dissipative evolution equations from their definitions.

Relativistic dissipative hydrodynamics from kinetic theory with relaxation-time approximation

Starting from Boltzmann equation with relaxation time approximation for the collision term and using Chapman-Enskog like expansion for distribution function close to equilibrium, we derive hydrodynamic evolution equations for the dissipative quantities directly from their definition. Although the form of the equations is identical to those obtained in traditional Israel-Stewart approaches employing Grads 14-moment approximation and second moment of Boltzmann equation, the coefficients obtained are different. In the case of one-dimensional scaling expansion, we demonstrate that our results are in better agreement with numerical solution of Boltzmann equation as compared to Israel-Stewart results. We also show that including approximate higher-order corrections in viscous evolution significantly improves this agreement, thus justifying the relaxation time approximation for the collision term.

Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods

Derivations of relativistic second-order dissipative hydrodynamic equations have relied almost exclusively on the use of Grads 14-moment approximation to write

Complete relativistic second-order dissipative hydrodynamics from the entropy principle

f(x,p)

Relativistic quantum transport coefficients for second-order viscous hydrodynamics

, the nonequilibrium distribution function in the phase space. Here we consider an alternative Chapman-Enskog-like method, which, unlike Grads, involves a small expansion parameter. We derive an expression for

Collective flow in event-by-event partonic transport plus hydrodynamics hybrid approach

f(x,p)

Relativistic third-order viscous corrections to the entropy four-current from kinetic theory

to second order in this parameter. We show analytically that while Grads method leads to the violation of the experimentally observed

New relativistic dissipative fluid dynamics from kinetic theory

1/\sqrt{m_T}

Particle production in relativistic heavy-ion collisions: A consistent hydrodynamic approach

scaling of the longitudinal femtoscopic radii, the alternative method does not exhibit such an unphysical behavior. We compare numerical results for hadron transverse-momentum spectra and femtoscopic radii obtained in these two methods, within the one-dimensional scaling expansion scenario. Moreover, we demonstrate a rapid convergence of the Chapman-Enskog-like expansion up to second order. This leads to an expression for

Relaxation-time approximation and relativistic third-order viscous hydrodynamics from kinetic theory

\delta f(x,p)