Geodesic
Application of the method of double-time Green's functions in the theory of migration
Teoretičeskaâ i matematičeskaâ fizika, Tome 14 (1973) no. 2, pp. 235-250

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The method of double-time Green's functions [1] is used to study the migration of vacancies in a one-dimensional lattice with allowance for deformation effects. A study is made of multiple phonon scattering on vacancies, and an equation for the corresponding transition matrix is constructed on the basis of the chain of equations for the Green's functions. For the diffusion coefficient an expression is obtained that allows for the rearrangement of the lattice vibrations due to the motion of a vacancy. 
@article{TMF_1973_14_2_a8,
     author = {Yu. A. Kashlev},
     title = {Application of the method of double-time {Green's} functions in the theory of migration},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {235--250},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_14_2_a8/}
}
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Yu. A. Kashlev. Application of the method of double-time Green's functions in the theory of migration. Teoretičeskaâ i matematičeskaâ fizika, Tome 14 (1973) no. 2, pp. 235-250. http://geodesic.mathdoc.fr/item/TMF_1973_14_2_a8/