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

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

《Chinese Journal of Physics》 2卷2期 (1964/10) Pp. 68-79

並列摘要

The effect of a light isotopic impurity atom on the energy flow in a one-dimensicnal system of coupled harmonic oscillators is investigated by means of the Schrödinger cccrdinates. Starting from the initial canonical ensemble which corresponds to such a thermodynamic state that half the system is at temperature T, and other half at temperature zero, the authors calculated the position- and the momentum-correlation functions of particles at any instant of time. Thus, it is shown that the average kinetic and potential energies of each particle in the infinitely large system approach a stationary state with a gap of energy distribution along the system at the impurity site. The result agrees essentially with that obtained by Kashiwamura and Teramoto who used trigonometric eigenfunctions of the system.Momentum-position ccrrelation functions are also calculated. The energy flow in the large system is derived from these, and it is shown that after a sufficiently long time the finite energy flow still exists at every site in the system though there is no temperature gradient at that site.The heat flow in the oscillator system with a light isotopic impurity is compared with that in the system with a heavy isotopic impurity. The similarity and difference at the final state between the two systems are also discussed.It should be also mentioned that our method used here is superior to the method of trigonometric eigenfunctions of the system; i.e. in cur method, (a) the initial condition is explicitly taken into account in the dynamical solution of the system, and (b) the ccvariance matrix in the initial ncrmal distribution function is diagonal& d, and so the calculation of the ccrrelation functions at any later time is very easily carried out.