  The quantum dynamics of a driven single-band tight-binding model with
different boundary conditions is considered. The relation between the
Hamiltonian describing the single-band tight-binding dynamics and the
Hamiltonian of a discrete-charge mesoscopic quantum circuit is elucidated. It
is shown that the former Hamiltonian, with Dirichlet boundary conditions, can
be considered as a realization of the deformed parafermionic polynomial
algebras.
