  We review recent results on the behaviour of the dielectric function of
cylindrical nano-organic materials at very low frequencies in a magnetic field.
For cylindrical structures - such as carbon nanotubes - the polarisability is
shown to be a discontinuous function of a longitudinal magnetic field where
plateau-like regions are separated by sudden jumps or peaks. A relation is
pointed out between each discontinuity in the polarisability and the cross-over
between ground and first excited states induced by the magnetic field. This one
to one correspondence suggests to use measurements of the dielectric function
in an applied magnetic field in order to obtain informations about the
electronic structures of cylindrical nanostructures. In addition, it is shown,
by studying finite graphene layers, that the measurement of the polarisability
in a magnetic field could be a powerful way for detecting possible edge-states
in amorphous carbon materials such as activated carbon fibres. Finally, the
importance of the electron-electron interaction is emphasised by discussing
examples of strongly interacting electrons on rings or cylinders, in the limit
of infinite interaction.
