caa a22 4500 475821920 CHVBK 20180406123821.0 cr unu---uuuuu 170329e20001201xx s 000 0 eng 10.1023/A:1011311915507 doi (NATIONALLICENCE)springer-10.1023/A:1011311915507 Electron Transfer through a One-Dimensional Fractal Structure [Elektronische Daten] [N. Chuprikov, D. Zhabin] An adequate model of electron tunneling through a self-similar fractal potential (SFP) defined on a Cantor set is extended to a generalized Cantor set. It is demonstrated that, as in a specific case, the Schrödinger equation for the SFP is reduced to a functional equation for the transfer matrix which admits solutions of three types. Two of them are single-parameter solutions corresponding to SFP barriers and lacunas with arbitrary powers. In both cases, the transfer matrices are nonanalytic in the long-wavelength region and have fractal dimensionalities there. The third solution type includes a unique solution corresponding to the SFP barrier with fixed power for a given barrier width. The corresponding transfer matrix is analytic at the point k = 0. It is shown that generally the SFP possesses only the property of approximate scale invariance on the generalized Cantor set in the long- and short-wavelength regions. Only the limiting SFP, whose fractal dimensionality is equal to unity, possesses the property of rigorous scale invariance irrespective of its power. It is shown that SFPs with identical fractal dimensionalities but different lacunas are described by different transfer matrices. Plenum Publishing Corporation, 2000 Chuprikov N. Tomsk State University, Russia aut Zhabin D. Tomsk State University, Russia aut Russian Physics Journal Kluwer Academic Publishers-Plenum Publishers 43/12(2000-12-01), 1026-1032 1064-8887 43:12<1026 2000 43 11182 https://doi.org/10.1023/A:1011311915507 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1011311915507 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chuprikov N. Tomsk State University, Russia aut NATIONALLICENCE 700 1- Zhabin D. Tomsk State University, Russia aut NATIONALLICENCE 773 0- Russian Physics Journal Kluwer Academic Publishers-Plenum Publishers 43/12(2000-12-01), 1026-1032 1064-8887 43:12<1026 2000 43 11182 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer