Statistical Dynamics of Systems of Interacting Oscillators

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Abstract
The dynamical behavior of systems of interacting harmonic oscillator is examined. Crystal lattices are examples of such systems. Description is made in terms of normal coordinates. It is assumed that energy is initially distributed canonically over the normal modes. The condition that the process is Markoffian is presented. As an example the behavior of one-dimensional lattice with a heavy isotope is discussed. The motion of the center of mass of a portion of a one-dimensional continuum is treated for comparison. Brownian motion of an oscillator is also discussed.

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