Kubo formulas for dispersion in heterogeneous periodic non-equilibrium systems

Abstract

We consider the dispersion properties of tracer particles moving in non-equilibrium heterogeneous periodic media. The tracer motion is described by a Fokker-Planck equation with arbitrary spatially periodic (but constant in time) local diffusion tensors and drift, eventually with the presence of obstacles. We derive a Kubo-like formula for the time dependent effective diffusion tensor valid in any dimension. From this general formula, we derive expressions for the late time effective diffusion tensor and drift in these systems. In addition, we find an explicit formula for the late finite time corrections to these transport coefficients. In one dimension, we give closed analytical formula for the transport coefficients. The formulas derived here are very general and provide a straightforward method to compute the dispersion properties in arbitrary non-equilibrium periodic advection-diffusion systems.

References in corpus (8)

• First-passage times in complex scale-invariant media
• Entropic transport: Kinetics, scaling and control mechanisms
• The Einstein relation generalized to non-equilibrium
• Entropic particle transport in periodic channels
• Colloids in light fields: particle dynamics in random and periodic energy landscapes
• Weak disorder strongly improves the selective enhancement of diffusion in a tilted periodic potential
• Approach to asymptotically diffusive behavior for Brownian particles in periodic potentials : extracting information from transients
• Approach to asymptotically diffusive behavior for Brownian particles in media with periodic diffusivities

Cited by in corpus (12)

• Controlling effective dispersion within a channel with flow and active walls
• Non-Gaussian diffusion near surfaces
• Geometry controlled dispersion in periodic corrugated channels
• The role of non-conservative scattering forces and damping on Brownian particles in optical traps
• How stickiness can speed up diffusion in confined systems
• Dispersion in two dimensional channels - the Fick-Jacobs approximation revisited
• Universal time dependent dispersion properties for diffusion in a one-dimensional critically tilted potential
• Generalized Taylor dispersion for translationally invariant microfluidic systems
• Dispersion in two-dimensional periodic channels with discontinuous profiles
• Effective diffusivity of Brownian particles in a two dimensional square lattice of hard disks
• Single-file diffusion in spatially inhomogeneous systems
• Interactions enhance dispersion in fluctuating channels via emergent flows