On the macroscopic quantization in mesoscopic rings and single-electron devices

Abstract

In this letter we investigate the phenomenon of macroscopic quantization and consider particle on the ring interacting with the dissipative bath as an example. We demonstrate that even in presence of environment, there is macroscopically quantized observable which can take only integer values in the zero temperature limit. This fact follows from the total angular momentum conservation combined with momentum quantization for bare particle on the ring. The nontrivial thing is that the model under consideration, including the notion of quantized observable, can be mapped onto the Ambegaokar–Eckern–Schon model of the single-electron box (SEB). We evaluate SEB observable, originating after mapping, and reveal new physics, which follows from the macroscopic quantization phenomenon and the existence of additional conservation law. Some generalizations of the obtained results are also presented.