# Energy growth of infinite harmonic chain under microscopic random influence

@article{Lykov2020EnergyGO, title={Energy growth of infinite harmonic chain under microscopic random influence}, author={Alexandr Lykov}, journal={Markov Processes and Related Fields}, year={2020}, volume={26}, pages={287-304} }

Infinite harmonic chains of point particles with finite range translation invariant interaction have considered. It is assumed that the only one particle influenced by the white noise. We studied microscopic and macroscopic behavior of the system's energies (potential, kinetic, total) when time goes to infinity. We proved that under quite general condition on interaction potential the energies grow linearly with time on macroscopic scale, and grow as $\ln(t)$ on microscopic scale. Moreover it…

## One Citation

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