非局域波函数电磁耦合测试的设计
Design of a test for the electromagnetic coupling of non-local wavefunctions
摘要：
最近已经证明，分数量子力学和凝聚态中的某些有效波函数不具有局部守恒电流;因此，它们与电磁场的耦合导致扩展的麦克斯韦方程组，具有非局部的，形式上简单的附加源项。求解这些方程的一般形式或找到解析近似是一项艰巨的任务，但数值解可以通过执行一些庞大的双延迟积分获得。我们专注于具体的实验情况下，可能允许检测这些（集体）波函数在铜氧化物超导体产生的异常准静态磁场。我们计算的空间依赖性的字段和它的振幅作为微观参数的函数，包括部分$η$的超导颗粒之间的约瑟夫森结，结的厚度$a$和大小$\varepsilon$的电流汇和源之间的约瑟夫森结不局部保守。结果表明，异常场实际上是可检测的宏观水平与敏感的实验，并可能是重要的，因为在微观水平上的虚电荷效应的典型的扩展麦克斯韦方程组。
英文摘要：
It has recently been proven that certain effective wavefunctions in fractional quantum mechanics and condensed matter do not have a locally conserved current; as a consequence, their coupling to the electromagnetic field leads to extended Maxwell equations, featuring non-local, formally simple additional source terms. Solving these equations in general form or finding analytical approximations is a formidable task, but numerical solutions can be obtained by performing some bulky double-retarded integrals. We focus on concrete experimental situations which may allow to detect an anomalous quasi-static magnetic field generated by these (collective) wavefunctions in cuprate superconductors. We compute the spatial dependence of the field and its amplitude as a function of microscopic parameters including the fraction $η$ of supercurrent that is not locally conserved in Josephson junctions between grains, the thickness $a$ of the junctions and the size $\varepsilon$ of their current sinks and sources. The results show that the anomalous field is actually detectable at the macroscopic level with sensitive experiments, and can be important at the microscopic level because of virtual charge effects typical of the extended Maxwell equations.
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