微观随机影响下无限长调和链的能量增长
Energy Growth of Infinite Harmonic Chain under Microscopic Random Influence
摘要：
考虑了有限程平移不变相互作用的点粒子的无限谐振子链。假设只有一个粒子受到白噪声的影响。我们研究了当时间趋于无穷大时系统能量（势能、动能、总能量）的微观和宏观行为。我们证明了在相当一般的相互作用势条件下，宏观尺度上能量随时间线性增长，微观尺度上能量按$\ln(t)$增长。此外，还证明了在这种非平衡条件下，该体系具有一定的均分性质。
英文摘要：
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 is turned out that the system exhibit some equipartition properties in this non equilibrium settings.
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