Statistical analysis of coupled oscillations with a single fixed endpoint and its application to carbon nanomaterials
Norio Inui
Abstract:Squared deviations from the equilibrium positions of one-dimensional coupled harmonic oscillators with fixed and free endpoints are calculated, and the time averages are expressed as a function of the initial displacements and velocities. Furthermore, we consider the averages of squared deviations over an ensemble of initial displacements and velocities, which distribute based on a product of the same distribution functions with variances of the initial coordinates σx
2 and velocities σv
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