  We present a new method for computing the wave function in the presence of
constraints. As an explicit example we compute the wave function for the many
electrons problem in coupled metallic rings in the presence of external
magnetic fluxes. For equal fluxes and an even number of electrons the
constraints enforce a wave function with a vanishing total momentum and a large
persistent current and magnetization in contrast to the odd number of electrons
where at finite temperatures the current is suppressed. We propose that the
even-odd property can be verified by measuring the magnetization as a function
of a varying gate voltage coupled to the rings. By reversing the flux in one of
the ring the current and magnetization vanish in both rings; this can be used
as a non-local control device.
