Supriya Ghosh (Editor)

Transport coefficient

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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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