The adiabatic heuristics:



Slowly varying perturbation: 
Slowly varying perturbation: one replaces the periodic operator with its dispersion 
relation  and  with the "slow" variable 
One "quantifies" the symbol:

Characteristic manifold:


The topology of these manifolds plays an important role: we assume 

The dispersion relation is multivalued; on the "real line", this function assumes exactly 
the values in the spectrum of the operator