(ALMOST) EVERYTHING YOU ALWAYS WANTED TO KNOW ABOUT THE CONDUCTANCE OF MESOSCOPIC SYSTEMS

Abstract

We present a systematic analysis of the average complex conductance of an ensemble of disordered mesoscopic conductors. It is argued that multiply connected Aharonov-Bohm rings are particularly amenable to this study, and reflect certain general features of the problem. Two ingredients are shown to be crucial in this context: (i) the ratio between the mean level spacing and the inelastic broadening of each level and (ii) the type of the statistical ensemble employed. Correspondingly, we distinguish between continuous and discrete spectrum limits and between canonical and grand canonical statistical ensembles. The conductance varies qualitatively as either of these two ingredients is changed. Analytical results for the conductance as a function of the magnetic flux, frequency and temperature are obtained in each limiting case. In particular, the sign of the d.c. (ω→0) magnetoconductance may change between the two limits. We also discuss the effect of electron-electron interaction.