One expects the spectrum to be located in exponentially small intervals located near the 
quantized energies. The size of these intervals is that of a tunneling effect controlled by
the actions.
The nature of the spectrum should be obtained by comparing tunneling coefficients.
But, in the case of two interacting bands, we have two sequences of intervals containing
spectrum.


Hence, there is a possibility of resonances between intervals from different sequences.
Let us recall the usual double well problem; consider the matrix , its eigen-
values are  where  and 
In the present case, one should rather consider the distance separating these intervals.

The tunneling effect relevant here is the horizontal tunneling  associated to