Calculating Fluctuations and Self-Correlations Numerically for Causal Charge Diffusion in Relativistic Heavy-Ion Collisions

Abstract

We study the propagation and diffusion of electric charge fluctuations in the Bjorken hydrodynamic model with both white and Catteneo noise using purely numerical methods. We show that a global lattice of noise fluctuations is required to fully calculate the two-point correlators of charge. We solve the stochastic differential equations that arise from the charge conservation equation on the lattice. We explicitly identify the self-correlation term in the case of Catteneo noise and provide a physical interpretation. We provide a numerical recipe to remove this contribution from the full two-point correlators. Finally, we calculate the balance functions for charged hadrons. By limiting the speed of signal propagation, we observe the expected narrowing of the balance functions after removing the self-correlations.

arXiv comment26 pages, 24 figures

References in corpus (18)

• Event-by-Event Fluctuations in Heavy Ion Collisions and the QCD Critical Point
• Non-Gaussian fluctuations near the QCD critical point
• 3+1D hydrodynamic simulation of relativistic heavy-ion collisions
• Slowing Out of Equilibrium Near the QCD Critical Point
• Hydro+: hydrodynamics with parametric slowing down and fluctuations near the critical point
• Electrical conductivity and charge diffusion in thermal QCD from the lattice
• Relativistic Theory of Hydrodynamic Fluctuations with Applications to Heavy Ion Collisions
• Diffusive dynamics of critical fluctuations near the QCD critical point
• Three-particle coincidence of the long range pseudorapidity correlation in high energy nucleus-nucleus collisions
• Thermal Conductivity and Chiral Critical Point in Heavy Ion Collisions
• Charge correlations using the balance function in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV
• Balance Functions from Au+Au, d+Au, and p+p Collisions at $\sqrt{s_{NN}}$ = 200 GeV
• Transits of the QCD Critical Point
• Hydrodynamics of charge fluctuations and balance functions
• Identifying the Charge Carriers of the Quark-Gluon Plasma
• Causal Baryon Diffusion and Colored Noise
• Causal Electric Charge Diffusion and Balance Functions in Relativistic Heavy Ion Collisions
• Untriggered di-hadron correlations in Pb-Pb collisions at $\sqrt{s_{NN}}=$ 2.76 TeV from ALICE

Cited by in corpus (7)

• The QCD phase diagram and Beam Energy Scan physics: a theory overview
• Progress and Challenges in Small Systems
• Numerically modeling stochastic inflation in slow-roll and beyond
• Stochastic hydrodynamics and hydro-kinetics: Similarities and differences
• Non-equilibrium cumulants within model A from crossover to first-order phase transition side
• Thermal fluctuations on the freeze-out surface of heavy-ion collisions and their impact on particle correlations
• Causal hydrodynamic fluctuations in a one-dimensional expanding system