The classical wave system has demonstrated itself as an excellent platform to realize and
investigate novel phenomena and physics. 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 physics and Casimir effect. The first part focuses on the impact of non
Hermitian ingredients on soliton formation and dynamics. By constructing a soliton phase diagram,
two distinct soliton phases and their transitions are identified. A Wannier-function-based nonlinear
Hamiltonian shows that soliton formation critically depends on how skin-mode localization and
band nonreciprocity suppress or enhance wave dispersion. Both soliton phases have been
demonstrated to be dynamically accessible from bulk and edge excitations. The second part
discusses 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 find that mesoscopic Casimir forces are sensitive to the surface
electron behavior, including spill-in and spill-out, as verified by the multiple scattering method and
proximity force approximation. The mechanism has finally been revealed as Casimir softening
distances rooted in quantum surface responses of electrons.
