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Area of Science:

  • Condensed Matter Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Shapiro steps are crucial in Josephson junctions and other nonlinear systems.
  • Thermal noise complicates the standard analysis of Shapiro steps.
  • Existing methods struggle with noise-induced step disappearance or melting.

Purpose of the Study:

  • Introduce a novel, practical method for analyzing Shapiro steps.
  • Provide experimentalists with an accessible tool for studying Shapiro steps under noisy conditions.
  • Demonstrate the utility of complexity measures in nonlinear dynamics.

Main Methods:

  • Utilized the dc+ac driven overdamped Frenkel-Kontorova model.
  • Calculated the Kolmogorov complexity of specific regions within the response function.
  • Analyzed the temperature dependence of Shapiro steps using the complexity measure.

Main Results:

  • Successfully detected Shapiro steps obscured by thermal noise.
  • Precisely measured the size of Shapiro steps.
  • Quantified the temperature dependence of Shapiro steps through complexity analysis.

Conclusions:

  • Kolmogorov complexity offers a robust alternative for Shapiro step analysis.
  • This complexity-based approach is practical for real systems with thermal noise.
  • The method enhances the study of nonlinear phenomena in the presence of dissipation and noise.