Divergence-type nonlinear conformal hydrodynamics

Abstract

Within the theoretical framework of divergence-type theories (DTTs), we set up a consistent nonlinear hydrodynamical description of a conformal fluid in flat space-time. DTTs go beyond second-order (in velocity gradients) theories, and are closed in the sense that they do not rely on adiabatic expansions. We show that the stress-energy tensor constructed from second-order conformal invariants is obtained from the DTT by a consistent adiabatic expansion. The DTT satisfies the Second Law, and is causal in a set of fluid states near equilibrium. Finally, we compare, analytically and numerically, the equations of motion of the DTT and its truncation to second-order terms for the case of boost invariant flow. Our numerical results indicate that the relaxation towards ideal hydrodynamics is significantly faster in the DTT than in the second-order theory. Not relying on a gradient expansion, our findings may be useful in the study of early-time dynamics and in the evolution of shock-waves in heavy-ion collisions.

Heavy quark collisional energy loss in the quark-gluon plasma including finite relaxation time

“…As mentioned in the Introduction, in this paper we shall use the polarization tensor that is derived from the effective hydrodynamic theory developed in Refs. [16][17][18][19]21]. This theory incorporates the effect of higher order velocity gradients into the hydrodynamic description of the QGP, thus extending its applicability to strongly out of equilibrium regimes (such as early time dynamics, most peripheral collisions and the borders of the fireball).…”

“…To compute the energy loss including a finite relaxation time τ π , we use the QGP polarization tensor that is derived from the effective hydrodynamic formalism developed by two of us in [16][17][18][19]. This model, which is constructed from the Entropy Production Variational Method [20], incorporates the effect of higher order velocity gradients into the hydrodynamic description of the QGP, thus extending the applicability of a macroscopic description to strongly out of equilibrium situations, such as early time dynamics of the plasma or the most peripheral collisions.…”

Anisotropic hydrodynamics for a mixture of quark and gluon fluids

“…One way to achieve this task is to compare the results of various hydrodynamic approaches [2][3][4][5][6][7][8][9][10][11][12], which differ by the number of terms included in the formalism and by the values of the transport coefficients, with the results of the underlying microscopic kinetic theory [13][14][15][16][17][18]. The latter is very often used as a staring point to derive the specific form of the evolution equations of relativistic hydrodynamics, however, several approximations done in such procedures may result in differences between the predictions of the kinetic theory and the hydrodynamic models constructed directly with its help.…”

Initial state fluctuations and final state correlations in relativistic heavy-ion collisions

“…(40) and (41), of which slightly different variants exist [58,60]. The extra terms typically involve time derivatives that transform the equations into relaxation equations that are then stable and solvable with numerical algorithms.…”