Transport coefficient

A Transport coefficient $\gamma$ can be expressed via a Green-Kubo relation:

\gamma =\int _{0}^{\infty }\langle {\dot {A}}(t){\dot {A}}(0)\rangle dt

where $A$ is an observable occurring in a perturbed Hamiltonian, $\langle \cdot \rangle$ is an ensemble average and the dot above the A denotes the time derivative.^[1] For times $t$ that are greater than the correlation time of the fluctuations of the observable the transport coefficient obeys a generalized Einstein relation:

2t\gamma =\langle |A(t)-A(0)|^{2}\rangle

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 $\eta ={\frac {1}{k_{B}TV}}\int _{0}^{\infty }dt\langle \sigma _{xy}(0)\sigma _{xy}(t)\rangle$
Electrical conductivity

References

↑ Water in Biology, Chemistry, and Physics: Experimental Overviews and Computational Methodologies, G. Wilse Robinson, ISBN 9789810224516, p. 80, Google Books

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Transport coefficient

Examples

See also

References