Quasiperiodically Forced Damped Pendula and Schrödinger Equations with Quasiperiodic Potentials: Implications of Their Equivalence

Abstract

Certain first-order nonlinear ordinary differential equations exemplified by strongly damped, quasiperiodically driven pendula and Josephson junctions are isomorphic to Schr\"odinger equations with quasiperiodic potentials. The implications of this equivalence are discussed. In particular, it is shown that the transition to Anderson localization in the Schr\"odinger problem corresponds to the occurrence of a novel type of strange attractor in the pendulum problem. This transition should be experimentally observable in the frequency spectrum of the pendulum or Josephson junction.