有限长非均匀约瑟夫森结中的钉扎磁通子
Pinned fluxons in a Josephson junction with a finite-length inhomogeneity
摘要：
我们考虑一个约瑟夫森结系统，安装了一个有限长度的不均匀性，无论是微电阻或微谐振器类型。该系统可以用一个正弦-戈登方程来模拟，用一个分段常数函数来表示变化的约瑟夫森隧穿临界电流。钉扎磁通子的存在依赖于不均匀性的长度、约瑟夫森隧穿临界电流的变化以及外加偏置电流。我们建立了一个系统可能无法维持钉扎通量，或者-例如，通过改变长度的不均匀性-可能会表现出各种不同类型的钉扎通量。我们的稳定性分析表明，稳定性的变化只能发生在临界点的长度的不均匀性的函数（哈密顿）能量密度内的不均匀性-我们明确确定的关系。结合延拓论和Sturm-Liouville理论，我们确定了所有构造的钉扎磁通子的稳定性。因此，如果给定系统能够维持至少一个钉扎通量，则恰好存在一个稳定的钉扎通量，即系统选择一个唯一的稳定钉扎构型。此外，它示出，无论是微电阻和微谐振器这种稳定的钉扎配置可能是非单调的东西，这是不可能的均匀的情况下。最后，它表明，在文献中的局部不均匀性的结果可以恢复作为我们的结果的限制微谐振器。
英文摘要：
We consider a Josephson junction system installed with a finite length inhomogeneity, either of microresistor or of microresonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent the varying Josephson tunneling critical current. The existence of pinned fluxons depends on the length of the inhomogeneity, the variation in the Josephson tunneling critical current and the applied bias current. We establish that a system may either not be able to sustain a pinned fluxon, or - for instance by varying the length of the inhomogeneity - may exhibit various different types of pinned fluxons. Our stability analysis shows that changes of stability can only occur at critical points of the length of the inhomogeneity as a function of the (Hamiltonian) energy density inside the inhomogeneity - a relation we determine explicitly. In combination with continuation arguments and Sturm-Liouville theory, we determine the stability of all constructed pinned fluxons. It follows that if a given system is able to sustain at least one pinned fluxon, there is exactly one stable pinned fluxon, i.e. the system selects one unique stable pinned configuration. Moreover, it is shown that both for microresistors and microresonators this stable pinned configuration may be non-monotonic - something which is not possible in the homogeneous case. Finally, it is shown that results in the literature on localised inhomogeneities can be recovered as limits of our results on microresonators.
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