标题： 低能下约瑟夫森隧道结耦合到传输线的精确对偶性 显示英文标题

标题： Exact Duality at Low Energy in a Josephson Tunnel Junction Coupled to a Transmission Line

摘要： 我们从理论上探讨了与有限长度、电荷偏置传输线耦合的约瑟夫森隧道结在低能区的行为，并将其与磁通偏置的情况进行了比较。 对于长度不断增加的传输线，我们证明可以通过电路参数的明确对偶变换，将电荷偏置构型下的低能电荷相关能量带精确映射到磁通偏置系统的那些能量带上。 在传输线无限长的极限情况下，边界条件的影响消失，两个电路都退化为电阻性短路约瑟夫森结。 这种收敛揭示了系统内在的自对偶性和临界行为。 我们关于电荷-磁通对偶性的精确表述为推广到更复杂的超导体-绝缘体相变提供了基础。 显示英文摘要

摘要： We theoretically explore the low-energy behavior of a Josephson tunnel junction coupled to a finite-length, charge-biased transmission line and compare it to its flux-biased counterpart. For transmission lines of increasing length, we show that the low-energy charge-dependent energy bands of the charge-biased configuration can be exactly mapped onto those of the flux-biased system via a well-defined duality transformation of circuit parameters. In the limit of an infinitely long transmission line, the influence of boundary conditions vanishes, and both circuits reduce to a resistively shunted Josephson junction. This convergence reveals the system's intrinsic self-duality and critical behavior. Our exact formulation of charge-flux duality provides a foundation for generalizations to more complex superconductor-insulator phase transitions.