Neutron scattering from quantum crystals
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The cross-section for neutron scattering from an arbitrarily anharmonic crystal is split up in the usual way into the Debye-Waller factor, the multiphonon background and the one-phonon peakS(1). The latter is shown to be built up by the expectation valueD of the displacement operator under the influence of a special mechanical force. The method of functional derivation applied to non-equilibrium Green's functions is used to find non-linear equations of motion forD. The renormalized force constants involved are also defined for singular interparticle potentials. The interference terms inS(1), which are expected to be important for a quantum crystal with large particle fluctuations, are related to the difference betweenD and its linear response value. Finally, the known sum-rules are derived in this formalism and prescriptions to determine the Debye-Waller factor fromD are given.
KeywordsNeural Network Complex System Nonlinear Dynamics Large Particle Force Constant
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