Complexity of Shapiro steps

TL;DR

This paper introduces a novel method using Kolmogorov complexity to analyze Shapiro steps in the presence of thermal noise, providing a practical tool for experimentalists to detect and measure these steps.

Contribution

It presents an innovative approach to analyze Shapiro steps by applying Kolmogorov complexity, overcoming challenges posed by thermal noise in traditional methods.

Findings

Kolmogorov complexity effectively detects Shapiro steps under thermal noise.

The method allows precise measurement of Shapiro step size.

Temperature dependence of Shapiro steps can be analyzed using this approach.

Abstract

We demonstrate on the example of the dc+ac driven overdamped Frenkel-Kontorova model that an easily calculable measure of complexity can be used for the examination of Shapiro steps in presence of thermal noise. In real systems, thermal noise causes melting or even disappearance of Shapiro steps, which makes their analysis in the standard way from the response function difficult. Unlike in the conventional approach, here, by calculating the Kolmogorov complexity of certain areas in the response function we were able to detect Shapiro steps, measure their size with desired precision and examine their temperature dependence. The aim of this work is to provide scientists, particularly experimentalists, an unconventional but a practical and easy tool for examination of Shapiro steps in real systems.