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Improvements of the equation of motion technique for disordered systems
Author(s) -
von Heimendahl L.
Publication year - 1978
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.2220860214
Subject(s) - trigonometric functions , representation (politics) , transformation (genetics) , simple (philosophy) , equations of motion , motion (physics) , function (biology) , differential equation , mathematics , numerical integration , mathematical analysis , classical mechanics , physics , geometry , biochemistry , chemistry , philosophy , epistemology , evolutionary biology , politics , biology , political science , law , gene
Abstract The equation of motion technique for the calculation of dynamical properties of large disordered systems is reconsidered and two improvements are proposed. Several procedures for the numerical integration of systems of second‐order differential equations are discussed and one particular efficient integration formula is selected. A modified cosine transformation for finite integration intervals is presented, which gives a positive, bell‐shaped function as a representation of the δ‐function instead of sin (ω T )/ω T . This allows an easier discussion of highly structured spectra. The results are demonstrated by a simple example.