具有含时通量的电路量子化：平行板SQUID
Circuit quantization with time-dependent flux:the parallel-plate SQUID
摘要：
量子线路理论已成为研究超导电路动力学的重要工具。最近，通过外部磁场来解释时间相关驱动的问题由Riwar-Dijuenzo在他们的论文"Circuit quantization with time-dependent磁场for realistic geometries“中提出，其中他们提出了一种技术来构建给定电路几何形状的低能哈密顿量，将与几何形状相互作用的外部磁场作为输入。这一结果概括了以前的努力，只处理离散电路。此外，它通过一个平行板SQUID电路的例子表明，分配个人，离散电容到每个单独的约瑟夫森结，提出的离散电路的治疗，只有可能的，如果我们允许负的，时间相关的，甚至奇异的电容。在这份报告中，我们提供了数值证据来证实这一结果进行有限差分模拟平行板SQUID。我们用均匀磁场提供连续的几何形状，我们改变磁场的分布，使得分配给每个约瑟夫森结的电容必须是负的，甚至是奇异的。因此，当我们允许磁场的分布随时间变化时，对于适当量化的时间相关电容的必要性自然出现。
英文摘要：
Quantum circuit theory has emerged as an essential tool for the study of the dynamics of superconducting circuits. Recently, the problem of accounting for time-dependent driving via external magnetic fields was addressed by Riwar-DiVincenzo in their paper - 'Circuit quantization with time-dependent magnetic fields for realistic geometries' in which they proposed a technique to construct a low-energy Hamiltonian for a given circuit geometry, taking as input the external magnetic field interacting with the geometry. This result generalises previous efforts that dealt only with discrete circuits. Moreover, it shows through the example of a parallel-plate SQUID circuit that assigning individual, discrete capacitances to each individual Josephson junction, as proposed by treatments of discrete circuits, is only possible if we allow for negative, time-dependent and even singular capacitances. In this report, we provide numerical evidence to substantiate this result by performing finite-difference simulations on a parallel-plate SQUID. We furnish continuous geometries with a uniform magnetic field whose distribution we vary such that the capacitances that are to be assigned to each Josephson junction must be negative and even singular. Thus, the necessity for time-dependent capacitances for appropriate quantization emerges naturally when we allow the distribution of the magnetic field to change with time.
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