Analytic properties of the lattice Green function
1972; IOP Publishing; Volume: 5; Issue: 1 Linguagem: Inglês
10.1088/0305-4470/5/1/011
ISSN2051-2155
Autores Tópico(s)Scientific Research and Discoveries
ResumoThe theory of functions of a complex variable is applied to show that the lattice Green function Gd(t;r) is an analytic function of the variable t, except when t is associated with a critical point. Here r denotes the position and t is the variable which represents the square of the frequency in lattice vibration problems, the energy in simplified problems of electron conduction and in spin wave theory. Singular behaviour of Gd(t:r) is given for t around its singular points omega c for the case where omega c are associated with the nondegenerate critical points. For the one dimensional system the singular behavior is also given for the degenerate critical points. Possibility of cancellation of the singular behaviour is suggested for some of the sites r. The singular behaviour derived for ImGd(t;0) is the same as than given by Van Hove.
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