A classical analog of the quantum mechanical model of three Josephson junctions in a loop

Abstract

It is shown that the time-dependent Schrödinger equation for a quantum mechanical system may be recast as a nonlinear flow if the Hamiltonian is a functional of the state of the system. This implies the possibility of deterministic chaos in this quantum mechanical system. If a classical Hamiltonian can be found that generates an identical flow, then a classical analog of the system exists. In particular, it is shown that such an analog exists for the quantum mechanical model of three Josephson junctions in a loop (3 J 2 L). This greatly facilitates the study of the trajectories of 3 J 2 L in the 4D phase space. There is a uniform stochastic web with unbounded anomalous diffusion in two of the four dimensions. This web has some striking differences from the 2D uniform stochastic webs of Zaslavsky and the 4D uniform stochastic webs of the authors.