News about Wave Behavior in Transparent, Periodical and Multichannel Structures

Zakhariev B. N., Chabanov V. M.

The hidden resonance nature of spectral gap formation by periodical potential perturbation has simple explanation. Wonderful coincidence of V(x) oscillation frequencies for the continuum of energy values results in unlimited (forbidden) increase of (x) oscillation amplitudes. This understanding unexpectedly appears a key moment also for explanation of behavior of physical solutions in allowed zones. There the violation of exact resonance leads to alteration of mutually compensating regimes of growth in opposite directions. So, the solutions in allowed zones do not swing with infinitely increasing amplitudes, but have beating. Also are demonstrated universal control algorithms of spectral zone boundaries up to the merging of neighbor conducting zones. It appears possible to control the rate of growth of solutions in any energy point of forbidden zone. It has important physical sense of the degree of forbiddenness control inside the spectral gap that determines the penetrability properties in configuration space. For example, in heterogeneous composition of intervals with different periodic structures the section with forbidden zone at chosen energy will serve as effective barrier between the sections with allowed zones, and we can change its transparency. Also are explained new transparency symmetries of separate parts of some potentials cut in arbitrary points. In addition some spectral peculiarities of multichannel structures are explained.

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