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arXiv 0710.5422cond-mat.supr-connlin.PS
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磁场中约瑟夫森结载流态问题的精确解析解

Exact analytical solution of the problem of current-carrying states of the Josephson junction in external magnetic fields

S. V. Kuplevakhsky, A. M. Glukhov

摘要:

本文从稳定性理论的观点出发,重新考虑了在外加磁场(H)和输运电流(J)作用下,任意长度W的约瑟夫森结的经典问题。特别是,我们推导出完整的无限集的精确解析解的相位差,描述的载流状态的结与任意W和任意模式的注入J。这些解决方案是参数化的两个自然参数:积分常数。它们在参数平面上的稳定区域的边界由相应的无穷多个精确泛函方程确定。被映射到物理平面(H,J),这些边界产生临界传输电流Jc对H的依赖性。与广泛传播的信念相反,即使对于任意小的W,精确的解析依赖性Jc=Jc(H)也被证明是多值的。更重要的是,精确解揭示了存在非量子化的约瑟夫森涡旋携带分数通量,并位于结的边缘之一,只要J是足够接近Jc的某些有限值的H。这一结论(以及其他精确的分析结果)说明了典型情况下的图形分析。

英文摘要:

The classical problem of the Josephson junction of arbitrary length W in the presence of externally applied magnetic fields (H) and transport currents (J) is reconsidered from the point of view of stability theory. In particular, we derive the complete infinite set of exact analytical solutions for the phase difference that describe the current-carrying states of the junction with arbitrary W and an arbitrary mode of the injection of J. These solutions are parameterized by two natural parameters: the constants of integration. The boundaries of their stability regions in the parametric plane are determined by a corresponding infinite set of exact functional equations. Being mapped to the physical plane (H,J), these boundaries yield the dependence of the critical transport current Jc on H. Contrary to a wide-spread belief, the exact analytical dependence Jc=Jc(H) proves to be multivalued even for arbitrarily small W. What is more, the exact solution reveals the existence of unquantized Josephson vortices carrying fractional flux and located near one of the junction edges, provided that J is sufficiently close to Jc for certain finite values of H. This conclusion (as well as other exact analytical results) is illustrated by a graphical analysis of typical cases.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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