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arXiv:2212.14029 · Physical Review C

Non-Gaussian fluctuation dynamics in relativistic fluids

Xin An, Gökçe Başar, Mikhail A. Stephanov, Ho-Ung Yee

Published Sep 19, 2023• 20 citations
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Abstract

We consider nonequilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation timescales, which emerges in the hydrodynamic regime near the critical point, to focus on the slowest mode such as the fluctuations of specific entropy, whose equilibrium magnitude, non-Gaussianity, and typical relaxation time are increasing as the critical point is approached. We derive evolution equations for the non-Gaussian correlators of this diffusive mode in an arbitrary relativistic hydrodynamic flow. We compare with the simpler case of the stochastic diffusion on a static homogeneous background and identify terms which are specific to the case of the full hydrodynamics with pressure fluctuations and flow.

DOI
10.1103/physrevc.108.034910

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We consider nonequilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation timescales, which emerges in the hydrodynamic regime near the critical point, to focus on the slowest mode such as the fluctuations of specific entropy, whose equilibrium magnitude, non-Gaussianity, and typical relaxation time are increasing as the critical point is approached. We derive evolution equations for the non-Gaussian correlators of this diffusive mode in an arbitrary relativistic hydrodynamic flow. We compare with the simpler case of the stochastic diffusion on a static homogeneous background and identify terms which are specific to the case of the full hydrodynamics with pressure fluctuations and flow.
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We describe numerical simulations of the stochastic diffusion equation with a conserved charge. We focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent $z\ensuremath{\simeq}3.972(2)$, which agrees with predictions of the epsilon expansion. We also study nonequilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.
Upon breaking the integrability, the equations of generalized hydrodynamics (GHD) are supplemented by a Boltzmann collision term. Such terms are typically complicated and stem from a perturbative treatment of integrability-breaking terms in the hamiltonian. In our work, we study a simplified version of the collision operator in a form of relaxation time approximation familiar from kinetic theory. We explicitly compute transport coefficients which characterize the Navier-Stokes (NS) hydrodynamic regime emerging at large space-time scales. We also thoroughly study the crossover between GHD and NS hydrodynamic descriptions, identifying relevant characteristic space-time scales for the transition. In particular, we show how the emergence of NS hydrodynamics is visible in dynamics of conserved and non-conserved charge densities, and in hydrodynamic two-point functions.