Quantum Dynamics of Nonlinear Oscillators

POSTER

Abstract

Motivated by an analogy to Josephson junctions, we studied the dynamics of a damped, driven pendulum in the quantum limit. We model the effects of damping by means of the quantum state diffusion method, in which the Hamiltonian in Schr\"odinger's equation is augmented by terms constructed from combinations of Lindblad operators. The dynamics were observed by looking at the time dependence of the expectation values of the pendulum's angular momentum and mechanical energy. We present our results. The next step is to couple two damped, driven quantum pendula and search for evidence of synchronization. This would suggest that it is possible to synchronize coupled small-area Josephson junctions, which must be treated in the quantum limit.

Authors

  • Brad Trees

    Ohio Wesleyan University

  • Kurt Wiesenfeld

    Miami University, Summa Health System, Akron, John Carroll University, Prof, Dr, BfS, Germany, Florida State University, Monmouth College, Ohio Wesleyan University, Kenyon College, University of Cincinnati, Brookhaven National Lab, University of Wisconsin Oshkosh, Dept. of Chermical Engineering, Carnegie Mellon University, Cleveland State University, The Neurological Institute, Epilepsy Center, Department of Neurology, Cleveland Clinic, Un. of Stockholm, The University of Akron, Case Western Reserve University, West Virginia University, Kalamazoo College and Editor, American Journal of Physics, Denison University, University of Southern Florida, Johannes-Gutenberg-Universitat, BfS (Germany), Shanghai Jiao Tong University, Department of Physics, West Virginia University, Kansas State University, The Pennsylvania State University, University of Wisconsin-Oshkosh, Purdue University, Saint Jospeh's College, University of Washington, Indiana University, University of Potsdam, Georgia Institute of Technology