Two important themes in nanoscale physics in the last two decades are correlations between electrons and mesoscopic ﬂuctuations. Here we review our recent work on the intersection of these two themes. The setting is the Kondo effect, a paradigmatic example of correlated electron physics, in a nanoscale system with mesoscopic ﬂuctuations; in particular, we consider a small quantum dot coupled to a ﬁnite reservoir (which itself may be a large quantum dot). We discuss three aspects of this problem. First, in the high-temperature regime, we argue that a Kondo temperature $T_K$ which takes into account the mesoscopic ﬂuctuations is a relevant concept: for instance, physical properties are universal functions of $T/T_K$. Secondly, when the temperature is much less than the mean level spacing due to conﬁnement, we characterize a natural cross-over from weak to strong coupling. This strong coupling regime is itself characterized by well-deﬁned single-particle levels, as one can see from a Nozières Fermi-liquid theory argument. Finally, using a mean-ﬁeld technique, we connect the mesoscopic ﬂuctuations of the quasiparticles in the weak coupling regime to those at strong coupling.
Volume 96, 2022
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