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Perturbative Approach to Dilute Off‐Diagonal Defects
Author(s) -
Wiecko C.
Publication year - 1988
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.2221480105
Subject(s) - diagonal , planar , diagrammatic reasoning , lattice (music) , inversion (geology) , phonon , diagonal matrix , series (stratigraphy) , mathematics , square lattice , statistical physics , physics , condensed matter physics , computer science , geometry , paleontology , computer graphics (images) , structural basin , acoustics , biology , programming language , ising model
A diagrammatic approach is developed to the problem of dilute concentration of off‐diagonal defects for short range interactions. The method is illustrated with the calculation of phonons when impurities that change the central force constant of the harmonic interaction with the nearest neighbors are present in three different structures: on the linear chain, on the square planar lattice, and the simple cubic structure. Systematic rules are obtained for the summation of the series. The procedure can inspire a more general algorithm for matrix inversion based on an eventually summable series.