摘要翻译：
我们研究了非线性振子在随机乘性噪声作用下的长时间行为，随机乘性噪声的谱密度（或功率谱）在高频以幂律衰减。当耗散可以忽略不计时，物理可观察到的振幅、速度和振荡器的能量随时间呈幂律增长。我们计算了相关的标度指数，我们表明它们的值依赖于外势的渐近行为和噪声的高频。我们的结果被推广到包括耗散效应和加性噪声。
---
英文标题：
《Anomalous diffusion in a random nonlinear oscillator due to high
  frequencies of the noise》
---
作者：
Kirone Mallick (CEA Saclay)
---
最新提交年份：
2007
---
分类信息：

一级分类：Physics        物理学
二级分类：Chaotic Dynamics        混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
--
一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--

---
英文摘要：
  We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical observables, such as the amplitude, the velocity and the energy of the oscillator grow as power-laws with time. We calculate the associated scaling exponents and we show that their values depend on the asymptotic behaviour of the external potential and on the high frequencies of the noise. Our results are generalized to include dissipative effects and additive noise.
---
PDF链接：
https://arxiv.org/pdf/710.4063