  We observe ``quantum'' properties of resonance equilibrium points and
resonance univariant submanifolds in the phase space. Resonances between
Birkhoff or Floquet--Lyapunov frequencies generate quantum algebras with
polynomial commutation relations. Irreducible representations and coherent
states of these algebras correspond to certain quantum nano-structure near the
classical resonance motion. Based on this representation theory and
nano-geometry, for equations of Schr\"odinger or wave type in various regimes
and zones (up to quantum chaos borders) we describe the resonance spectral and
long-time asymptotics, resonance localization and focusing, resonance adiabatic
and spin-like effects. We discuss how the mathematical phase space
nano-structures relate to physical nanoscale objects like dots, quantum wires,
etc. We also demonstrate that even in physically macroscale Helmholtz channels
the resonance implies a specific quantum character of classical wave
propagation.
