Premium
Localization of Electron Wave Functions in One‐Dimensional Disordered Systems
Author(s) -
Hermann H.
Publication year - 1974
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220660112
Subject(s) - diagonal , eigenvalues and eigenvectors , exponential function , wave function , lattice (music) , physics , exponential decay , electron , function (biology) , mathematics , mathematical analysis , mathematical physics , quantum mechanics , geometry , acoustics , evolutionary biology , biology
Results are presented of numerical calculations of the eigenvalues and eigenvectors of one‐dimensional systems with diagonal and off‐diagonal disorder. Two possible definitions of the localization length are discussed. Using a formula of Thouless the quantity L exp ( E ) describing the exponential decay of a wave function far away from the localization centre is calculated for chains containing up to 400 lattice sites. The energy dependence of L exp for off‐diagonal disorder differs from that of the well‐known case of diagonal disorder. It is found that the wave functions of an infinite one‐dimensional system with statistically distributed hopping terms are extended at least over an half infinite part of the complete infinite system.