What is the complex impedance of a fully coherent quantum resistance-capacitance (RC)
circuit at gigahertz frequencies in which a resistor and a capacitor are connected in series?
While Kirchhoff's laws predict addition of capacitor and resistor impedances, we report on
observation of a different behavior. The resistance, here associated with charge relaxation,
differs from the usual transport resistance given by the Landauer formula. In particular, for a
single-mode conductor, the charge-relaxation resistance is half the resistance quantum …

Violation of Kirchhoff's laws for a coherent RC circuit - Sorbonne Université …