Complexity of Shapiro steps

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.

Description of Shapiro steps on the potential energy surface of a Frenkel–Kontorova model, Part II: free boundaries of the chain

“…12, also fulfill a periodicity, with a larger s value, and may be with a further factor by the period, 2π. So, such a relation may be not the criterion for the existence of the Shapiro steps, as it is pretended in former papers [2,14,16,17,33], to name but a few.…”

“…It holds x i < x i+1 for the ordered chain. A boundary condition like x N = x 1 [16] is not correct. The free end points of the chain determine the current average…”

“…It is worth noting that the kink, as well as the antikink form a spontaneous symmetry break of the given chain [31] since the global minimum is a symmetric structure which is the case here. The symmetry break for both LEPs is outside of an assumption of a 'symmetry operation' in an FK chain in references [2,14,16,32], see also Sect. 5.…”

“…It is a mathematical tool for the description of an abstract sliding along the tilted site-up potential. Nevertheless, the abstract velocity also originates the Shapiro steps being the yield of many former references [2,14,16,17,33], to mention but a few. Usually in former works the unspecific washboard force [34]…”

“…Note that other site-up potentials, or another choice of the external forces do not destroy the pattern of Shapiro steps [2,16,17,33]. If there is any appropriate PES then the periodic ac-force will find a region in the mountains of the PES where the lock-down of a Shapiro step can happen.…”