Kondo effect and spin-charge separation in quantum dots

The Kondo effect in a quantum dot is discussed. In the standard Coulomb blo ckade setting, tunneling between the dot and the leads is weak, the number of electrons in the dot is well-defined and discrete; the Kondo effect may be considered in the framework of the conventional one-level Anderson impur ity model. It turns out however, that the Kondo temperature T-K in the case of weak tunneling is extremely low. In the opposite case of almost reflect ionless single-mode junctions connecting the dot to the leads, the average charge of the dot is not discrete. Surprisingly, its spin may remain quanti zed: s = 1/2 or s = 0, depending (periodically) on the gate voltage. Such a "spin-charge separation" occurs because, unlike an Anderson impurity, a qu antum dot carries a broad-band, dense spectrum of discrete levels. In the d oublet state, the Kondo effect develops with a significantly enhanced T-K. Like in the weak-tunneling regime, the enhanced T-K exhibits strong mesosco pic fluctuations. The statistics of the fluctuations is universal, and rela ted to the Porter-Thomas statistics of the wave function fluctuations.