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Shapiro steps and chaos in the Frenkel-Kontorova model with substrate lateral vibration.
Phys Rev E
October 2022
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.
Numerical simulations are used to examine the dynamics of the dc-driven Frenkel-Kontorova model with an oscillation substrate subjected to lateral periodic excitations in overdamped and underdamped cases, respectively. The results reveal that the system exhibits frequency locking and chaotic behaviors due to the fact that the lateral vibration of the substrate potential introduces an additional frequency and degree of freedom into the system. In the overdamped case, we show that the appearance of subharmonic Shapiro steps can be attributed to the deformation of the substrate potential or inertia.
View Article and Find Full Text PDFInertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis.
Phys Rev E
February 2019
BLTP, JINR, Dubna, Moscow Region, 141980, Russian Federation.
The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure.
View Article and Find Full Text PDFNon-equilibrium charge and spin transport in superconducting-ferromagnetic-superconducting point contacts.
Philos Trans A Math Phys Eng Sci
August 2018
Department of Microtechnology and Nanoscience - MC2, Chalmers University of Technology, 412 96 Göteborg, Sweden
The conventional Josephson effect may be modified by introducing spin-active scattering in the interface layer of the junction. Here, we discuss a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin that precesses with the Larmor frequency due to an external magnetic field. This magnetically active interface results in a time-dependent boundary condition with different tunnelling amplitudes for spin-up and -down quasi-particles and where the precession produces spin-flip scattering processes.
View Article and Find Full Text PDFSubharmonic Shapiro steps of sliding colloidal monolayers in optical lattices.
J Phys Condens Matter
April 2016
Dipartimento di Fisica, Università di Milano, Via Celoria 16, 20133 Milano, Italy. International School for Advanced Studies (SISSA), Via Bonomea 265, I-34136 Trieste, Italy.
We investigate theoretically the possibility to observe dynamical mode locking, in the form of Shapiro steps, when a time-periodic potential or force modulation is applied to a two-dimensional (2D) lattice of colloidal particles that are dragged by an external force over an optically generated periodic potential. Here we present realistic molecular dynamics simulations of a 2D experimental setup, where the colloid sliding is realized through the motion of soliton lines between locally commensurate patches or domains, and where the Shapiro steps are predicted and analyzed. Interestingly, the jump between one step and the next is seen to correspond to a fixed number of colloids jumping from one patch to the next, across the soliton line boundary, during each ac cycle.
View Article and Find Full Text PDFFarey sequence in the appearance of subharmonic Shapiro steps.
Phys Rev E Stat Nonlin Soft Matter Phys
May 2015
"Vinča" Institute of Nuclear Sciences, Laboratory for Theoretical and Condensed Matter Physics 020, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia.
The largest Lyapunov exponent has been examined in the dynamical-mode locking phenomena of the ac+dc driven dissipative Frenkel-Kontorova model with deformable substrate potential. Due to deformation, large fractional and higher order subharmonic steps appear in the response function of the system. Computation of the largest Lyapunov exponent as a way to verify their presence led to the observation of the Farey sequence.
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