Analytical results on the periodically driven damped pendulum. Application to sliding charge-density waves and Josephson junctions

Journal Article · Mon Oct 01 04:00:00 EDT 1984 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.30.3722· OSTI ID:6233136

Azbel, M Y; Bak, P

The differential equation epsilonphi-dieresis+phi-dot-(1/2)..cap alpha.. sin(2phi) = I+summation/sub n/ = -infinity/sup infinity/A/sub n/delta(t-t/sub n/) describing the periodically driven damped pendulum is analyzed in the strong damping limit epsilon<<1, using first-order perturbation theory. The equation may represent the motion of a sliding charge-density wave (CDW) in ac plus dc electric fields, and the resistively shunted Josephson junction driven by dc and microwave currents. When the torque I exceeds a critical value the pendulum rotates with a frequency ..omega... For infinite damping, or zero mass (epsilon = 0), the equation can be transformed to the Schroedinger equation of the Kronig-Penney model. When A/sub n/ is random the pendulum exhibits chaotic motion. In the regular case A/sub n/ = A the frequency ..omega.. is a smooth function of the parameters, so there are no phase-locked subharmonic plateaus in the ..omega..(I) curve, or the I-V characteristics for the CDW or Josephson-junction systems. For small nonzero epsilon the return map expressing the phase phi(t/sub n/+1) as a function of the phase phi(t/sub n/) is a one-dimensional circle map. Applying known analytical results for the circle map one finds narrow subharmonic plateaus at all rational frequencies, in agreement with experiments on CDW systems.

• Research Organization: Department of Physics and Astronomy, University of Tel Aviv, Ramat Aviv, Israel
• OSTI ID: 6233136
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Journal Name: Phys. Rev. B: Condens. Matter; (United States) Vol. 30:7; ISSN PRBMD
• Country of Publication: United States
• Language: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DAMPING
DIFFERENTIAL EQUATIONS
ELECTRIC CONDUCTIVITY
ELECTRIC FIELDS
ELECTRICAL PROPERTIES
EQUATIONS
EQUATIONS OF MOTION
JOSEPHSON JUNCTIONS
JUNCTIONS
MAPS
MODULATION
OSCILLATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PENDULUMS
PHYSICAL PROPERTIES
PLASMA WAVES
SUPERCONDUCTING JUNCTIONS
USES