Abstract

We explain Shapiro steps in a Frenkel–Kontorova (FK) model for a 1D chain of particles with free boundaries. The action of an external alternating force for the oscillating structure of the chain is important here. The different ’floors’ of the potential energy surface (PES) of this model play an important role. They are regions of kinks, double kinks, and so on. We will find out that the preferable movements are the sliding of kinks or antikinks through the chain. The more kinks / antikinks are included the higher is the ’floor’ through the PES. We find the Shapiro steps moving and oscillating anywhere between the floors. They start with a single jump over the highest SP in the global valley through the PES, like in part I of this series. They finish with complicated oscillations in the PES, for excitations directly over the critical depinning force. We use an FK model with free boundary conditions. In contrast to other results in the past, for this model, we obtain Shapiro steps in an unexpected, inverse sequence. We demonstrate Shapiro steps for a case with soft ’springs’ between an 8-particle FK chain.

Graphic abstract

中文翻译：

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Shapiro在Frenkel-Kontorova模型的势能面上的台阶描述，第二部分：链的自由边界

摘要

我们在Frenkel-Kontorova（FK）模型中解释具有自由边界的一维粒子链的Shapiro步骤。在此，外部交变力对于链条的摆动结构的作用很重要。该模型的势能面（PES）的不同“底面”起着重要作用。它们是扭结，双重扭结等区域。我们将发现，较好的运动是扭结或反扭结在链条中的滑动。包含的纠结/抗纠结越多，则通过PES的“地板”越高。我们发现Shapiro台阶在地板之间的任意位置移动和振荡。他们首先通过PES跳过了全球山谷中最高的SP，就像本系列的第一部分一样。他们在PES中伴随着复杂的振荡而结束，直接在临界销钉力上产生激励。我们使用带有自由边界条件的FK模型。与过去的其他结果相反，对于此模型，我们以意外的逆序获得了Shapiro步骤。我们演示了在8粒子FK链之间带有软“弹簧”的情况下的Shapiro步骤。

图形摘要