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 $\eta = \frac{1}{k_BT V}\int_0 ^\infty dt \langle \sigma_{xy}(0) \sigma_{xy} (t) \rangle$
• Electrical conductivity

See also

• Linear response theory

References

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