  We extend the correspondence between the Renn-Lubensky Twist-Grain-Boundary-A
phase in chiral liquid crystals and the Abrikosov mixed state in
superconductors to dynamical aspects. We find that for a TGB sample with free
boundaries, an external electric field applied along the helical axis induces a
uniform translational motion of the grain boundary system - an analogue of the
well-known mixed state flux flow. Likewise, an analogue of the mixed state
Nernst effect is found. In much the same way in which the flux flow carries
intercore electric fields generating Joule heat in an otherwise
dissipation-free system, the grain boundary flow carries along polarized
charges, resulting in a finite electric conductivity in a ferroelectric.

Chemical Physics;Chemical Physics