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arXiv · 1808.09359

Freezing of the optical--branch energy in a diatomic FPU chain

Alberto Mario Maiocchi
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Abstract

We study the exchange of energy between the modes of the optical branch and those of the acoustic one in a diatomic chain of particles, with masses $m_1$ and $m_2$. We prove that, at small temperature and provided $m_1\gg m_2$, for the majority of the initial data the energy of each branch is approximately constant for times of order $\beta^{S/2}$, where $S=\lfloor \sqrt{m_1/m_2}/2\rfloor$ and $\beta$ is the inverse temperature. The result is uniform in the thermodynamic limit.

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Alberto Mario Maiocchi. 2018-08-28. Freezing of the optical--branch energy in a diatomic FPU chain. https://doi.org/10.1007/s00220-019-03381-z

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