  We study the quantum transport through entropic barriers induced by hardwall
constrictions of hyperboloidal shape in two and three spatial dimensions. Using
the separability of the Schrodinger equation and the classical equations of
motion for these geometries we study in detail the quantum transmission
probabilities and the associated quantum resonances, and relate them to the
classical phase structures which govern the transport through the
constrictions. These classical phase structures are compared to the analogous
structures which, as has been shown only recently, govern reaction type
dynamics in smooth systems. Although the systems studied in this paper are
special due their separability they can be taken as a guide to study entropic
barriers resulting from constriction geometries that lead to non-separable
dynamics.
