Frequency dependence of giant Shapiro steps in ordered and site-disordered proximity-coupled Josephson-junction arrays

Effects of noise on interference phenomena in the presence of subharmonic Shapiro steps

Existence and properties of the Shapiro steps in the presence of noise have been studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. The results have shown that the influence of noise on interference phenomena is determined by the presence and the size of half-integer steps. Since half-integer steps are more affected by noise, and the properties of harmonic steps are directly correlated with the size of half-integer steps, noise will have completely different effects on the harmonic steps if half-integer steps are present. As temperature increases, in the amplitude dependence of the step width, deviation from the well-known Bessel-like oscillations has been observed, and three different types of behavior have been classified. In the influence of noise on the frequency dependence of the steps, appearance of oscillations and strong influence of half-integer steps on their form have been observed.

Existence and stability of the resonant phenomena in the dc- and ac-driven overdamped Frenkel-Kontorova model with the incommensurate structure

Dynamical mode-locking phenomena in the incommensurate structures of the dc- and ac-driven overdamped Frenkel-Kontorova model are studied by molecular-dynamics simulations. The obtained results have shown that Shapiro steps exhibit significantly different amplitude and frequency dependence from the one observed in the commensurate structures. Due to the incommensurability of the system the special symmetry of the motion of particles is broken, and in the amplitude dependence of Shapiro steps, this will result in the appearance of anomalies and deviation from the well-known Bessel-like behavior. In the frequency or period dependence, oscillations have been observed in the high-amplitude limit; however, they exhibit strong anomalies compared with those in the commensurate structures. The oscillatory behavior and the anomalies have been also be revealed in the (F(ac),F) and the (ν(0),F) phase diagrams where several phases are defined.

Frequency dependence of the subharmonic Shapiro steps

Frequency dependence of the subharmonic Shapiro steps has been studied in the ac driven overdamped Frenkel-Kontorova model with deformable substrate potential. As potential gets deformed, in addition to the harmonic steps, subharmonic steps appear in the number and size that increase as the frequency of the external force increases. It was found that size of both harmonic and subharmonic steps strongly depend on the frequency where in the high-amplitude limit oscillatory dependence appears. When expressed as a function of period these oscillations of the step size with frequency have the same form as the oscillations of the step size with amplitude. Deformation of the potential has strong influence on these oscillations, and as in the case of amplitude dependence, with the increase of deformation, the same three distinctive types of behavior have been classified.

Noise effects in the ac-driven Frenkel-Kontorova model

The noise effects on dynamical-mode-locking phenomena in the ac-driven dissipative Frenkel-Kontorova model are studied by molecular-dynamics simulations. It was found that the noise strongly influences the properties of the Shapiro steps and the way they respond to the changing of system parameters. The increase of temperature produces the melting of the Shapiro steps, while the critical depinning force is significantly reduced. The oscillatory form of the amplitude dependence is strongly affected where the Bessel-like form changes as the temperature increases. In the frequency dependence of the Shapiro steps, due to the decrease of the dc threshold value, noise may transfer the system to the high-amplitude regime where oscillations of the step width with frequency or period of the ac force appear. These phenomena will additionally destabilize the steps in real systems and significantly limit the region of parameters where dynamical-mode-locking phenomena could be observed.

Amplitude and frequency dependence of the Shapiro steps in the dc- and ac-driven overdamped Frenkel-Kontorova model

The amplitude and frequency dependence of dynamical mode locking phenomena in the dc- and ac-driven overdamped Frenkel-Kontorova model is studied by molecular-dynamics simulations. It was found that the Shapiro steps and the critical depinning force exhibit very complex behavior. The form of amplitude dependence is determined by the frequency of ac force, where the Bessel-type oscillations appear at the high frequencies. With a changing of frequency, after initial increase, the critical depinning force saturates, while the step width remains strongly frequency dependent even at the high frequencies. The dependence of frequency is strongly influenced by the amplitude of ac force where, in the large amplitude regime, the oscillations of the step width and the critical depinning force have been observed at the low frequencies. In the physical processes that stay behind amplitude and frequency oscillations of the step size, an analogy between the influence of amplitude and the period of the ac force is revealed. These oscillations are directly related to the existence and the stability of the interference phenomena in the real systems.