Topolectrical circuit theory and realizations of topological, non-linear, and non-Hermitian phenomena

Abstract: Electrical circuits offer a unique platform to explore physical phenomena, from topology to non-Hermitian effects. Investigations of the fundamental properties of this metamaterial platform are crucial to distinguish observed/measured quantities from intrinsic circuit responses. In this thesis, we delve into the analysis of voltage and impedance responses and their role in unveiling complex dynamics and profound physical principles. We reveal that even the simplest one-dimensional circuits exhibit intriguing voltage profiles. Our study of multi-dimensional and multi-structural lattice models shows size-dependent impedance responses, which challenge our current textbook knowledge. Building on these insights, we will present non-linear and non-Hermitian circuit applications, showcasing how electrical circuits provide a suitable platform for realizing intriguing physical phenomena.