Stochastic hydrodynamics and hydro-kinetics: Similarities and differences

Aritra De, Chun Shen, Joseph I. Kapusta

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

The hydro-kinetic formalism has been used as a complementary approach to solving the stochastic differential equations (SDE) corresponding to noisy hydrodynamics. The hydro-kinetic formalism consists of a deterministic set of relaxation type equations that tracks the evolution of two-point correlation functions of stochastic hydrodynamic quantities. Hence they are comparatively easier to solve than the SDEs, which are computationally intensive and need to deal with arbitrarily large gradients. This work compares the two approaches for the propagation and diffusion of conserved charge fluctuations in the Bjorken hydrodynamic model. For white noise, the two approaches agree. For colored Catteneo noise, which is causal, the two approaches diverge. This is because white noise only induces two-point correlations, while Catteneo noise also induces higher-order correlations. This difference is quantified from the effects of causal evolution and influence from higher-order correlations induced by the Catteneo noise.

Original languageEnglish (US)
Article number054903
JournalPhysical Review C
Volume106
Issue number5
DOIs
StatePublished - Nov 2022

Bibliographical note

Funding Information:
The authors thank Derek Teaney and Mayank Singh for their helpful discussions. This work was supported by the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under DOE Contracts No. DE-FG02-87ER40328 and No. DE-SC0021969. C.S. acknowledges a DOE Office of Science Early Career Award. We acknowledge the Minnesota Supercomputing Institute (MSI) at the University of Minnesota for providing resources that contributed to the research results reported within this paper.

Publisher Copyright:
© 2022 American Physical Society.

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