Multiplicative noise and the diffusion of conserved densities

Abstract

Stochastic fluid dynamics governs the long time tails of hydrodynamic correlation functions, and the critical slowing down of relaxation phenomena in the vicinity of a critical point in the phase diagram. In this work we study the role of multiplicative noise in stochastic fluid dynamics. Multiplicative noise arises from the dependence of transport coefficients, such as the diffusion constants for charge and momentum, on fluctuating hydrodynamic variables. We study long time tails and relaxation in the diffusion of a conserved density (model B), and a conserved density coupled to the transverse momentum density (model H). Careful attention is paid to fluctuation-dissipation relations. We observe that multiplicative noise contributes at the same order as non-linear interactions in model B, but is a higher order correction to the relaxation of a scalar density and the tail of the stress tensor correlation function in model H.

arXiv commentadd an appendix, updated the references, 17 pages, 5 figures

References in corpus (11)

• Lectures on hydrodynamic fluctuations in relativistic theories
• Effective field theory for dissipative fluids (II): classical limit, dynamical KMS symmetry and entropy current
• Diffusive dynamics of critical fluctuations near the QCD critical point
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Theory of diffusive fluctuations
• Towards an effective action for relativistic dissipative hydrodynamics
• Viscous Hydrodynamics and the Quark Gluon Plasma
• Transits of the QCD Critical Point
• Shear viscosity from thermal fluctuations in relativistic conformal fluid dynamics
• Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes
• Multiplicative Noise: Applications in Cosmology and Field Theory

Cited by in corpus (10)

• Evolution of Non-Gaussian Hydrodynamic Fluctuations
• Hydrodynamic effective field theory and the analyticity of hydrostatic correlators
• Holographic Schwinger-Keldysh field theory of SU(2) diffusion
• Long-time tails in the SYK chain from the effective field theory with a large number of derivatives
• Positive magnetoresistance induced by hydrodynamic fluctuations in chiral media
• Dynamical critical fluctuations near the QCD critical point with hydrodynamic cooling rate
• N-particle irreducible actions for stochastic fluids
• 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
• Dynamics of the conserved net-baryon density near QCD critical point within inhomogeneous quark-gluon plasma profile