Non-Hermitian dynamics in a simple LC circuit and beyond!

Over the past 20 years, systems with Non-Hermitian Hamiltonians have changed from mathematical curiosity to a vibrant research area spanning classical and quantum domains. In quantum cases, it is due to the novel dynamics that arises from exceptional-point (EP) degeneracies of their complex eigenvalues. In classical wave systems with PT-symmetric Hamiltonians, it is due to novel effects that includes enhanced sensitivity, topological transfer, and breakdown of bulk-boundary correspondence. After a brief overview of "non-Hermitian Hamiltonians”, I will show that simple problems - such such an LC circuit with time-dependent parameters - can be mapped onto systems with effective, non-Hermitian Hamiltonians (Phys. Rev. Applied 18, 054034 (2022)). I will discuss their key surprising properties, and show how they can be realized across quantum (Nat. Phys, 15, 1232 (2019);Nat. Commun. 10, 855 (2019); Nature 557, 660 (2018)) and classical platforms such as electrical circuits, lasers, and shallow-water-waves.  I will conclude the talk with open areas where these ideas may break new ground, and the unique role played by computational approach and young students in this broad field of research.