Microscopic Derivation of Causal Diffusion Equation using Projection Operator Method

Abstract

We derive a coarse-grained equation of motion of a number density by applying the projection operator method to a non-relativistic model. The derived equation is an integrodifferential equation and contains the memory effect. The equation is consistent with causality and the sum rule associated with the number conservation in the low momentum limit, in contrast to usual acausal diffusion equations given by using the Fick's law. After employing the Markov approximation, we find that the equation has the similar form to the causal diffusion equation. Our result suggests that current-current correlations are not necessarily adequate as the definition of diffusion constants.

10 pages, 1 figure, Final version published in Phys. Rev. E

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• Dynamic universality class of the QCD critical point
• Causal Diffusion and the Survival of Charge Fluctuations in Nuclear Collisions
• Enhancement of Critical Slowing Down in Chiral Phase Transition -- Langevin Dynamics Approach --
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• Bulk Viscosity and Relaxation Time of Causal Dissipative Relativistic Fluid Dynamics
• Microscopic formula for transport coefficients of causal hydrodynamics
• Incorporating Memory Effects in Phase Separation Processes
• Shock propagation and stability in causal dissipative hydrodynamics
• Relativistic Brownian motion: From a microscopic binary collision model to the Langevin equation
• Formulating Viscous Hydrodynamics for Large Velocity Gradients
• Shear viscosity, Bulk viscosity and Relaxation Times of Causal Dissipative Relativistic Fluid-Dynamics at Finite Temperature and Chemical Potential
• Uncertainty Relations in Hydrodynamics
• Dissipation and memory effects in pure glue deconfinement
• Open Problems in Hydrodynamical Approach to Relativistic Heavy Ion Collisions
• New Formulation of Causal Dissipative Hydrodynamics: Shock wave propagation
• Viscosity of non equilibrium hot $\&$ dense QCD drop formed at LHC
• Dynamic density correlations in a baryon rich fluid using Mori-Zwanzig-Nakjima projection operator method
• Memory Effects and Transport Coefficients for Non-Newtonian Fluids