Beyond Closed Wave Systems: Non-Hermiticity and Nanoscale Casimir Force

The classical wave system has proven to be an excellent platform for realizing novel phenomena that may be challenging to implement in other physical systems experimentally. The bedrocks are macroscopic quantities obtained from the homogenization or mean-field treatment. However, it usually deals with Hermitian problems and averages out fluctuations. Therefore, the presentation will cover two topics: non-Hermitian (NH) physics and mesoscopic Casimir effect. The first part will focus on the spectral topology, which deals with complex energy patterns and their interaction with the wavefunction. I will begin with the order-3 exceptional lines (EL3s) embedded in order-2 exceptional surfaces (ES2s). The eigenvalue winding number becomes poorly defined, so we adopt the resultant manifold to detect only the EL3 but ignore the ES2, which allows the diagnosis of topological currents of the EL3s, enabling the prediction of their evolution under perturbations. Next, I will devote myself to higher-dimensional skin effects (SEs), including geometry-dependent and algebraic SE in mechanics and photonics. Physical understanding and solving the eigenstates will be presented in detail afterward. The second part will discuss nanoscale Casimir force softening from quantum surface responses (QSRs). A three-dimensional conformal mapping method has been established by embedding mesoscopic boundary conditions of electromagnetic fields. It then uncovers that nanoscale Casimir forces are sensitive to the surface electron behavior, and the mechanism results from QSRs effectively alter the distance seen by the Casimir interaction. With such an understanding, a recipe to handle the nanoscale Casimir force between nanoscale complex objects has been provided.