Classical analogs of mesoscopic quantum phenomena

Abstract

An important aspect of mesoscopic electronic systems is that the electrons maintain their phase coherence and propagate as waves. The resulting behavior is complicated by disorder, time-dependent scattering sites and many-electron effects (possibly modeled with a nonlinear wave equation). Studying the latter effects theoretically or experimentally in mesoscopic electronic systems is difficult. However, it is possible to contrive classical wave systems which precisely duplicate the salient features of the quantum electron problem, and which may be readily studied experimentally. This paper will describe the use of such systems to study phonon assisted hopping, the effects of nonlinearity on Anderson localization, the effects of Penrose tile symmetry, noise in mesoscopic electronics, ‘superdiffusion’, and to study an aspect of the discrepancy between theory and experiment for normal electron persistent currents in mesoscopic rings.