2003/11/19 by L. A. Dmitrieva, Л. А. Дмитриева, Dmitrieva, L. A. +2 · 1 citation
Engineering · Physics and Astronomy · #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Molecular Junctions and Nanostructures #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall
paper · pdf · doi:10.48550/arxiv.cond-mat/0311468
14 pages, LaTex
arxiv created 2003/11/19 · openalex publication_date 2003/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A local perturbation theory for the spectral analysis of the Schrödinger operator with two periodic potentials whose periods are commensurable has been constructed. It has been shown that the perturbation of the periodic 1D Hamiltonian by an additional small periodic potential leads to the following spectral deformation: all gaps in the spectrum of the unperturbed periodic Hamiltonian bear shifts while any band splits by arising additional gaps into a set of smaller spectral bands. The spectral shift, the position of additional gaps and their widths have been calculated explicitly. The applications to the operational regime of a nanoelectronic device based on Mott-Peierls stimulated transition have also been discussed.