  We study electrical and thermoelectrical properties for a double quantum dot
system. We consider the cases of both single-level and multilevel quantum dots
whatever the way they are coupled, either in a series or in a parallel
arrangement. The calculations are performed by using the nonequilibrium Green
function theory. In the case of a single-level double quantum dot, the problem
is exactly solvable whereas for a multilevel double quantum dot, an analytical
solution is obtained in the limit of energy-independent hopping integrals. { We
present a detailed discussion about} the dependences of electrical conductance,
zero-frequency charge susceptibility and Seebeck coefficient on the gate
voltages applied to the dots, allowing us to derive the charge stability
diagram. The findings are in agreement with the experimental observations
notably with the occurrence of successive sign changes of the Seebeck
coefficient when varying the gate voltages. We interpret the results in terms
of the bonding and antibonding states produced by the level anticrossing effect
which occurs in the presence of a finite interdot coupling. We show that at
equilibrium the boundary lines between the domains with different dot
occupancies in the charge stability diagram, take place when the bonding and
antibonding state levels are aligned with the chemical potentials in the leads.
Finally the total dot occupancy is found to be considerably reduced in the case
in parallel compared with the case in series, { whenever} the level energies in
each dot are equal. We interpret this dip as a direct manifestation of the
interference effects occurring in the presence of the two electronic
transmission paths provided by each dot.
