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Prog. Theor. Phys. Vol. 24 No. 6 (1960) pp. 1349-1368

Time Dependent Problems of the Localized Lattice Vibration

Ei Teramoto and Shozo Takeno^*

Physics Department, Kyoto University, Kyoto
^*Osaka Institute of Technology, Osaka

(Received August 22, 1960)

Abstract:

The time dependent problems of the vibrational motion are investigated for the cases of infinitely extended one-dimensional lattice which contains one or two impurity atoms (isotopes). Starting from the equations of motion of these systems, we derive the integral equations which show various dependent properties of the lattice vibration of these perturbed one-dimensional lattices. Namely, the asymptotic solutions of these integral equations represent the localized vibration which is preserved by the impurity atom when its mass is smaller than that of base atoms. The integral equations are actually solved by means of the perturbation calculation and also by the use of Laplace transforms, and the behaviors of the lattice vibration especially the capture of the vibrational energy by the impurity atoms, are examined.

URL : http://ptp.ipap.jp/link?PTP/24/1349/
DOI : 10.1143/PTP.24.1349

[ Full Text PDF : FREE ACCESS (897K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. Progress of Theoretical Physics Vol. 26 No. 4 (1961) pp. 568-569 :

   Motion of an Impurity Atom in One-Dimensional Lattice

   Shohei Kashiwamura

2. Progress of Theoretical Physics Vol. 27 No. 3 (1962) pp. 571-588 :

   Statistical Dynamical Behaviors of a One-Dimensional Lattice with an Isotopic Impurity

   Shohei Kashiwamura

3. Progress of Theoretical Physics Vol. 28 No. 1 (1962) pp. 33-79 :

   Energy Spectrum of Lattices with Defects. II

   Shozo Takeno

4. Progress of Theoretical Physics Vol. 28 No. 6 (1962) pp. 1059-1064 :

   Heat Flow in the Linear Chain of Harmonically Coupled Particles

   Ei Teramoto

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