  Using the pseudospin representation and the SU(2) phase operators we
introduce a complex parameter to characterize both infinite and finite
superconducting systems. While in the bulk limit the parameter becomes
identical to the conventional order parameter, in the nanoscopic limit its
modulus reduces to the number parity effect parameter and its phase takes
discrete values. We evaluate the Josephson coupling energy and show that in
bulk superconductor it reproduces the conventional expression and in the
nanoscopic limit it leads to quantized Josephson effect. Finally, we study the
phase flow or dual Josephson effect in a superconductor with fixed number of
electrons.
