Some Considerations Related to the Quantization of Charge in Mesoscopic Systems

Abstract

Over the last few years there have been a large number of theoretical and experimental papers concerned with the consequences, in various types of mesoscopic systems, of the fact that electric charge is quantized in units of e. In this lecture I do not intend to go into the details of the calculations of these effects—something for which there are several people at this School much better qualified than me. Rather, I would like to take a hard look at some of the fundamental conceptual aspects of this type of problem, and in particular at the question: To what extent do the familiar concepts of macroscopic electrical engineering such as voltage, current, capacitance etc. have a meaning when we describe our system in quantum mechanical terms? In particular, just how far do we have to take our book-keeping as regards, say, the actual nature of a “current source” we intend to use to drive our quantum mechanical system? To many working in this area, perhaps these questions seem trivial and the answers to them obvious. As far as I am concerned, they are far from trivial, and while a sustained attempt to answer them may not alter the results of existing calculations, or at least not qualitatively, I believe it will give us significant understanding that may be useful elsewhere in mesoscopic physics.