Speaker
Description
We study an approach for simulating the stochastic relativistic advection-diffusion equation based on the Metropolis algorithm. We show that the dissipative dynamics of the boosted fluctuating fluid can be simulated by making random transfers of charges between fluid cells, interspersed with ideal hydrodynamic time steps. The random charge transfers are accepted or rejected in a Metropolis step using the entropy as a statistical weight. This procedure reproduces the expected strains of dissipative relativistic hydrodynamics in a specific (and non-covariant) hydrodynamic frame known as the density frame. Numerical results, both with and without noise, are presented and compared to relativistic kinetics and analytical expectations. An all order resummation of the density frame gradient expansion reproduces the covariant dynamics in a specific model. Finally, we outline in detail the algorithm for the relativistic Navier-Stokes equations. In contrast to all other numerical approaches to relativistic dissipative fluids, the formalism we present is strictly first order in gradients and has no non-hydrodynamic modes. The physical naturalness and simplicity of the Metropolis algorithm, together with its convergence properties, make it a promising tool for simulating stochastic relativistic fluids heavy ion collisions and critical phenomena in the relativistic
domain.
