Influence of the Noise Spectrum on Stochastic Acceleration

TL;DR

This paper investigates how the noise spectrum influences the long-term energy growth and phase space distribution in a nonlinear Langevin system, revealing dependence on potential and noise characteristics.

Contribution

It introduces an effective Markovian framework to analytically describe the asymptotic behavior of nonlinear Langevin equations with Gaussian noise, including dissipation effects.

Findings

Energy grows as a power-law with an anomalous exponent.

Asymptotic phase space distribution is derived analytically.

Results depend on the confining potential and noise frequency distribution.

Abstract

We use an effective Markovian description to study the long-time behaviour of a nonlinear second order Langevin equation with Gaussian noise. When dissipation is neglected, the energy of the system grows as with time a power-law with an anomalous scaling exponent that depends both on the confining potential and on the high frequency distribution of the noise. The asymptotic expression of the Probability Distribution Function in phase space is calculated analytically. The results are extended to the case where small dissipative effects are taken into account.