• Accepted Paper

Time-domain transient growth in non-Hermitian cascaded LC circuits

Liangliang Ye, Mingyong Ye, Xiang Chen, Gongwei Lin, and Xiumin Lin

Phys. Rev. E - Accepted 1 October, 2026

DOI: https://doi.org/10.1103/g48r-vzs5

Abstract

Transient growth is a counterintuitive dynamical process in which a system state or observable undergoes pronounced temporary amplification during its evolution, even in the presence of substantial dissipation. Here, we demonstrate time-domain transient growth in non-Hermitian cascaded LC circuits with unidirectional coupling. Under short-pulse excitation, the terminal-voltage envelope exhibits a cascade-length-dependent delayed build-up. As the number of dissipative resonators increases, the main growth window shifts systematically to later times, while the terminal-envelope growth rate exhibits a dramatic increase and the transient peak becomes substantially larger. Comparisons between uniform-loss and nonuniform-loss configurations show that the delayed growth persists when the exact exceptional-point (EP) condition is lifted, indicating that it is governed mainly by unidirectional cascaded coupling and is not restricted to an exact EP condition. These results establish unidirectionally coupled non-Hermitian circuits as a circuit-realizable platform for studying and engineering time-domain transient growth, thereby connecting non-Hermitian physics with transient growth.

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