Semiclassical Structure of the Advection--Diffusion Spectrum in Mixed Phase Spaces
This paper investigates the spectral structure of the two-dimensional advection-diffusion operator in mixed phase spaces at large Peclet numbers, revealing that the spectrum is organized into distinct families of eigenmodes governed by local Lagrangian geometry and semiclassical analogies, which leads to persistent modal competition rather than single-mode dominance in finite-time dynamics.