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. 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

See also

• Linear response theory