The classical wave system has demonstrated itself as an excellent platform to realize novel phenomena that may be challenging to implement in other physical systems experimentally. The bedrock principle is to utilize the 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 interplay with the wavefunction. We begin with geometry-dependent skin effect (GDSE). Its realization in the reciprocal system requires mismatching macroscopic symmetry mismatches with lattice symmetry, highlighting the role of geometry in higher-dimensional NH physics. We next devote ourselves to discussing 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. The second part will discuss the influence of the metal's surface electrons on Casimir forces. A three-dimensional frame transformation method has been established by embedding mesoscopic boundary conditions of electromagnetic fields. We uncover that mesoscopic Casimir forces are sensitive to the surface electron behavior, such as the spill-in and spill-out, verified by the multiple scattering method and proximity force approximation.

Please contact phweb@ust.hk should you have questions about the talk.