Emulation of quantum mechanical billiards by electrical resonance circuits

Abstract

We propose that a two-dimensional electric network may be used for fundamental studies of wave function properties, transport, and related statistics. Using Kirchhoff's current law and the j omega method we find that the network is analogous to a discretized Schrödinger equation for quantum billiards and dots. Thus complex electric potentials play the role of quantum mechanical wave functions. Ways of realizing the electric network are discussed briefly. The role of symmetries is outlined, and a direct way of selecting states with a given symmetry is presented.