  Coherent resonant tunneling through an artificial molecule of quantum dots in
an inhomogeneous magnetic field is investigated using an extended Hubbard
model. Both the multiterminal conductance of an array of quantum dots and the
persistent current of a quantum dot molecule embedded in an Aharanov-Bohm ring
are calculated. The conductance and persistent current are calculated
analytically for the case of a double quantum dot and numerically for larger
arrays using a multi-terminal Breit-Wigner type formula, which allows for the
explicit inclusion of inelastic processes. Cotunneling corrections to the
persistent current are also investigated, and it is shown that the sign of the
persistent current on resonance may be used to determine the spin quantum
numbers of the ground state and low-lying excited states of an artificial
molecule. An inhomogeneous magnetic field is found to strongly suppress
transport due to pinning of the spin-density-wave ground state of the system,
and giant magnetoresistance is predicted to result from the ferromagnetic
transition induced by a uniform external magnetic field.
