Dynamic correlations of the classical and quantum Toda lattices

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Abstract
The dynamic correlations of classical and quantum Toda lattices are approached by moment expansion. For the classical model, the moments of the spectral shape of the displacement-displacement correlation function are exactly calculated up to the eighth one, while, for the quantum system, their evaluation is limited to the sixth one, using the effective-potential method in low-coupling approximation. The spectral shape is calculated using the continued-fraction expansion. The relevance of quantum effects is clearly shown, in dependence on temperature and quantum coupling. At all wave vectors, the spectral shape presents a single-peak structure, both in the classical and in the quantum regime.