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Prog. Theor. Phys. Vol. 34 No. 4 (1965) pp. 534-538
On the Asymptotic Green's Function in an n-Dimensional Lattice Model
P. M. Mathews and
M. S. Seshadri
Department of Physics, University of Madras, Madras 25, India
(Received June 19, 1965)
Abstract:
The asymptotic form of the Green's function representing the effect of a point imperfection (isotopic impurity) in an n-dimensional lattice is obtained by the use of a multiple saddle-point method. It is shown to be an improvement over an earlier evaluation, in the case of localized vibrational modes with frequency not too close to the largest band frequency of the lattice.
URL :
http://ptp.ipap.jp/link?PTP/34/534/
DOI : 10.1143/PTP.34.534
References:
- P. M. Mathews, M. S. Seshadri and R. Vijayalakshmi, Z. Angew. Math. Mech. 45 (1965), 209.
-
E. W. Montroll and R. B. Potts, Phys. Rev. 103 (1956), 72[APS].
- E. W. Montroll, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, 1955), p. 209.
- S. Takeno, Prog. Theor. Phys. 28 (1962), 33[PTP].
- A. A. Maradudin, E. W. Montroll and G. H. Weiss, Theory of Lattice Dynamics in the Harmonic Approximation, Suppl. 3, Solid State Physics Series (Academic Press, 1963), p. 153.
