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

Anders Bondeson; Edward Ott; Thomas M. Antonsen, Jr

doi:10.1103/PhysRevLett.55.2103

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

Anders Bondeson, Edward Ott, and Thomas M. Antonsen, Jr.

Phys. Rev. Lett. 55, 2103 – Published 11 November 1985

Abstract

Certain first-order nonlinear ordinary differential equations exemplified by strongly damped, quasiperiodically driven pendula and Josephson junctions are isomorphic to Schrödinger equations with quasiperiodic potentials. The implications of this equivalence are discussed. In particular, it is shown that the transition to Anderson localization in the Schrödinger 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.

Received 28 June 1985

DOI:https://doi.org/10.1103/PhysRevLett.55.2103

Authors & Affiliations

Anders Bondeson^*, Edward Ott^†, and Thomas M. Antonsen, Jr.^†

Institute for Theoretical Physics, University of California, Santa Barbara, California 93106

^*Permanent address: Institute for Electromagnetic Field Theory, Chalmers University of Technology, S41296 Göteborg, Sweden.
^†Permanent address: Departments of Electrical Engineering and of Physics, University of Maryland, College Park, Md. 20742.