Dynamical Structure Factor of a Classical Anharmonic Oscillator

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Abstract
As a prototype of anharmonic lattice vibrations, a classical oscillator moving in the anharmonic potential V(x) = Ax4 + Bx2 is studied. In this model, exact expression for the dynamical structure factor, which is proportional to the cross section of neutron inelastic scattering, can be obtained in the framework of classical statistical mechanics. By the use of this expression, the dynamical structure factor is numerically calculated. It is shown that the magnitude of momentum transfer selects particular oscillations and seriously affects the structure of the spectra.

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