• Corpus ID: 216330632

# 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}
}
• A. Lykov
• Published 2 May 2020
• Physics
• Markov Processes and Related Fields
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…
1 Citations
• Mathematics
• 2022
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with ﬁnite support and local external force (stationary stochastic process) acting only on

## References

SHOWING 1-10 OF 14 REFERENCES

• Mathematics
• 2013
It is known that a linear hamiltonian system has too many invariant measures, thus the problem of convergence to Gibbs measure has no sense. We consider linear hamiltonian systems of arbitrary finite
• Physics, Engineering
• 2018
We consider dynamics of a one-dimensional harmonic chain with harmonic on-site potential subjected to kinematic and force loadings. Under kinematic loading, a particle in the chain is displaced acc...
• Physics
• 2017
We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles
AbstractPROF. R. H. FOWLER'S monumental work on statistical mechanics has, in this the second edition, in his own modest words, been rearranged and brought more up to date. But the new volume is much
If challenged to describe the subject-matter of this book while standing on one foot, one might say: It is the study of the behavior (mostly at infinity) of the solutions of equations of the form
* Deterministic and Random Oscillators * White and Colored Noise * Brownian Motion * Overdamped Harmonic Oscillator with Additive Noise * Overdamped Harmonic Oscillator with Multiplicative Noise *
The interest in asymptotic analysis originated from the necessity of searching for approximations to functions close the point(s) of interest. Suppose we have a function f(x) of single real parameter