Nonlinear noninertial response of a quantum Brownian particle in a tilted periodic potential to a strong ac force as applied to a point Josephson junction

William T. Coffey, Yuri P. Kalmykov, Serguey V. Titov, and Liam Cleary
Phys. Rev. B 79, 054507 – Published 10 February 2009

Abstract

The quantum Smoluchowski equation for the reduced Wigner function in configuration space pertaining to the quantum Brownian motion of a particle in a tilted cosine potential in the high dissipation (or noninertial) limit as applied to a model point Josephson junction (namely, a resistively shunted junction in the presence of noise and an arbitrarily large microwave ac driving current) is considered. The solution of the resulting recurrence relations for the Fourier amplitudes of the statistical moments describing the nonlinear dynamics of the junction (ignoring the capacitance) is obtained using the matrix continued fractions previously developed for the stationary ac field solution of the corresponding classical problem. Quantum effects in the nonlinear response of the junction to an ac microwave current of arbitrary amplitude (nonlinear microwave impedance, frequency dependence of the dc current-voltage characteristic, etc.) are estimated.

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  • Received 4 November 2008

DOI:https://doi.org/10.1103/PhysRevB.79.054507

©2009 American Physical Society

Authors & Affiliations

William T. Coffey1, Yuri P. Kalmykov2, Serguey V. Titov3, and Liam Cleary1

  • 1Department of Electronic and Electrical Engineering, Trinity College, Dublin 2, Ireland
  • 2Laboratoire de Mathématiques, Physique et Systèmes, Université de Perpignan, 52, Avenue de Paul Alduy, 66860 Perpignan Cedex, France
  • 3Kotel’nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Vvedenskii Square 1, Fryazino, 141190, Russian Federation

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Vol. 79, Iss. 5 — 1 February 2009

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