Transport coefficient - Alchetron, The Free Social Encyclopedia

A Transport coefficient γ can be expressed via a Green-Kubo relation:

γ = ∫ 0 ∞ ⟨ A ˙ ( t ) A ˙ ( 0 ) ⟩ d t ,

where A is an observable occurring in a perturbed Hamiltonian, ⟨ ⋅ ⟩ is an ensemble average and the dot above the A denotes the time derivative. For times t that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized Einstein relation:

2 t γ = ⟨ | A ( t ) − A ( 0 ) | 2 ⟩ .

Transport coefficients measure how rapidly a perturbed system returns to equilibrium.

Examples

Diffusion constant, relates the flux of particles with the negative gradient of the concentration (see Fick's laws of diffusion)

Heat transport coefficient

Mass transport coefficient

Shear Viscosity η = 1 k B T V ∫ 0 ∞ d t ⟨ σ x y ( 0 ) σ x y ( t ) ⟩

Electrical conductivity

References

Transport coefficient Wikipedia

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