  In this work,we study the Kondo effect of a quantum dot (QD) connected to
leads and to a discrete set of one particle states provided by a quantum box
represented by a quantum ring (QR) pierced by a magnetic flux side attached to
the QD. The interplay between the bulk Kondo effect and the so called Kondo box
regime is studied. In this system the QR energies can be continuously modified
by the application of the magnetic field. The crossover between these two
regimes is analyzed by changing the connection of the QD to the QR from the
weak to the strong coupling regime. In the weak coupling regime, the
differential conductance develops a sequence of Fano-Kondo antiresonances due
to destructive interferences between the discrete quantum ring levels and the
conducting Kondo channel provided by the leads. In the strong coupling regime
the differential conductance has very sharp resonances when one of the Kondo
discrete sub-level characterizing the Kondo box is tunned by the applied
potential. The conductance, the current fluctuations and the Fano coefficient
result to be the relevant physical magnitudes to be analyzed to reveal the
physical properties of these two Kondo regimes and the crossover region between
them. The results were obtained by using the Slave Boson Mean Field Theory
(SBMFT).
