Effect of an Isotopic Impurity on the Energy Flow in a System of One-Dimensional Coupled Harmonic Oscillators

小林圭子(Keiko Kobayasi) ； 瀧澤英一(Éiiti Takizawa)

《Chinese Journal of Physics》 2卷1期 (1964/04) Pp. 10-22

並列摘要

linearSchröd- of coupled harmonic oscillators is investigated by means of the inger coordinates. Assuming such an initial canonical ensemble that half the system is at temperature T and other half at temperature zero, the correlation functions of particles in the system are calculated as functions of time. Thus, it is shown that the average kinetic and potential energies of each particle in the infinitely large system approach different stationary values in both sides of the impurity atom, and that the system approach a stationary state with a gap of energy distribution along the system at the impurity site. This result agrees with that obtained by Kashiwamura and Teramoto by means of trigonometric eigenfunctions of the dynamical system.The elements of position-velocity correlation matrix are also calculated. The energy flow in the large system is derived from these, and it is shown that even after a sufficiently long time the finite energy flow still exists at every point of the system though there is no temperature gradient at that point.It should be mentioned, however, that the method we used here is easier to calculate and simpler by far than that by means of the trigonometric eigenfunctions of the dynamical system.