Stochastic baryon charge transport in relativistic hydrodynamics

We utilize stochastic hydrodynamics to study correlations and fluctuations of baryon charge in high-energy heavy-ion collisions. The baryon charge fluctuations are important observables to probe the quantum chromodynamics (QCD) phase diagram, yet a dynamical description with stochastic hydrodynamics remains challenging due to numerical instabilities and high computational demands. In this work, we employ a linearized approach, allowing us to separately simulate the background energy-momentum evolution of a charge-neutral fluid and the stochastic baryon transport processes, thereby largely reducing computational cost while maintaining sufficient accuracy. We implement this linearized stochastic charge evolution in the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>3</a:mn><a:mo>+</a:mo><a:mn>1</a:mn><a:mi mathvariant="normal">D</a:mi></a:mrow></a:math> viscous hydrodynamic code , and compare numerical results to (semi-)analytical solutions for stochastic charge transport in Bjorken flow. We find that it nicely describes the two-point correlation of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mrow><d:mn>1</d:mn><d:mo>+</d:mo><d:mn>1</d:mn><d:mi mathvariant="normal">D</d:mi></d:mrow></d:math> analytical solutions for various equations of state and transport coefficients. In particular, the hydrodynamic calculations demonstrate how different rapidity separations probe charge fluctuations originating at different times of the evolution. We also investigate the net baryon correlations after the Cooper-Frye freeze out, which show good consistency with the analytical calculations and indicate that these fluctuation-induced correlations are sensitive to the baryon diffusion coefficient.