Abstract
We present a self-consistent theory for the dynamical one-phonon structure factor in anharmonic crystals. The theory is the phonon analogue of the mode-coupling theory of liquid dynamics of Götze and his coworkers. Starting point is the lattice dynamics treatment based on the Mori- Zwanzig technique as formulated by Götze and Michel. We apply the theory to the one-dimensional (1d) Lennard-Jones chain and show that the nonlinear mode-coupling equations can be readily solved in the time domain. The vertices entering the equations as input are calculated exactly by a Monte Carlo technique. We compare our findings with molecular dynamics (MD) simulations and the results of other theoretical approaches.
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We use the same notation as in [18] und [19]
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Dedicated to Wolfgang Götze on the occasion of his 60th birthday
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Scheipers, J., Schirmacher, W. Mode-coupling theory for the lattice dynamics of anharmonic crystals: self-consistent damping and the 1d Lennard-Jones chain. Z. Phys. B 103, 547–553 (1997). https://doi.org/10.1007/s002570050409
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DOI: https://doi.org/10.1007/s002570050409