重访阻尼谐振子：通往平衡的最快路径
经典物理
2023-07-11 v2
摘要
理论上，阻尼谐振子的解渐近趋于平衡（即零能态）而从未精确达到，且临界阻尼解比欠阻尼或过阻尼解更快趋于平衡。实验上，用该模型描述的系统在系统能量降至低于对应于测量仪器能量分辨率的某阈值时达到平衡。我们证明，人们（几乎）总能找到一个最优欠阻尼解，其比所有其他欠阻尼解以及临界阻尼解更早达到该能量阈值，无论该阈值多小。我们也评论了对于一类特定初值条件的例外：此时某个特定过阻尼解比所有其他解更早达到平衡态。我们通过实验证实了部分发现。
引用
@article{arxiv.2301.08222,
title = {Damped harmonic oscillator revisited: the fastest route to equilibrium},
author = {Karlo Lelas and Nikola Poljak and Dario Jukić},
journal= {arXiv preprint arXiv:2301.08222},
year = {2023}
}
备注
9 pages of main text + supplementary material. The biggest changes compared to the previous version are in section IIIC, that section has been somewhat shortened and written more clearly. Also, some typos and similar errors in supplementary materials have been corrected. The paper is accepted for publication in American Journal of Physics