2003/02/27 by B. N. Zakhariev, Zakhariev, B. N., V. M. Chabanov +1
Physics and Astronomy · #FOS: Physical sciences #Nonlinear Photonic Systems #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum chaos and dynamical systems #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0302195
16 pages, 9 figures; some improvements in the text are made
openalex publication_date 2003/02/27 · arxiv created 2003/04/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the mechanism of gap formation has a resonance nature. The special real fundamental solutions were discovered which `paradoxically' have knot distribution with a period coinciding with that of potential at all energies of the whole lacuna interval. In terms of these solutions resonance gap appearance gets the most direct explanation: ever repeating hits by the potential result in exponential increase (decrease) of the wave amplitudes in the forbidden zones. The analogous alternating hits from opposite sides are responsible for the wave beatings in allowed zones. The inversion technique gives rise to zone control algorithms - shifting chosen boundaries of spectral bands, changing degree of zone forbiddenness. All this cannot be achieved by the previous Bloch theory.