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Electric circuit analog of Landau-Zener tunneling using time-varying elements

Landau-Zener tunneling (LZT) is a fundamental dynamical phenomenon, ubiquitous in various quantum systems. Here, we propose a time-varying electric circuit to address the question of whether the quantum LZT can occur in classical systems. Although the underlying differential equation of motion is quite different from the Schrödinger equation and the instantaneous frequency spectrum of the proposed circuit is not linear, the probability of the LZT in circuits (circuit LZT for short), based on our generalized definition for norm-unconserved systems, still follows the laws of the LZT in quantum systems, codetermined by the linear sweeping rate $α'$ and the frequency gap $Δ$, i.e., approaching the analytical value $\exp(-πΔ^2/2α')$, regardless of whether the coupling is reciprocal or nonreciprocal. The deep relationship between the circuit LZT and its quantum counterpart can be established through a linearization and block-diagonalization process. Our proposal provides a general method for simulating time-dependent quantum models using time-varying electric circuits, which has been lacking in previous studies, and paves the way for studying more complicated LZT and other dynamical phenomena in circuits and other classical systems.