随机非线性振子中高频噪声引起的反常扩散
Anomalous diffusion in a random nonlinear oscillator due to high frequencies of the noise
摘要：
本文研究了随机乘性噪声作用下非线性振子的长时间行为，噪声的谱密度（或功率谱）在高频下按幂律衰减。当耗散可以忽略时，振子的振幅、速度和能量等物理量随时间呈幂律增长。我们计算相关的标度指数，我们表明，它们的值取决于外部潜在的渐近行为和噪声的高频率。我们的结果被推广到包括耗散效应和加性噪声。
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.
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