Stochastic parametric modulation of linear and non-linear oscillators: Perturbation theory of the response function
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913490520768512 |
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| author | Dey, Sourin Bhattacharjee, Jayanta K. |
| author_facet | Dey, Sourin Bhattacharjee, Jayanta K. |
| contents | We study a stochastically driven, damped nonlinear oscillator whose frequency is modulated by a white or coloured noise. Using diagrammatic perturbation theory, we find that in the absence of nonlinearity, parametric modulation by a coloured noise can lead to a Kapitza pendulum-like stabilization of an unstable configuration provided the noise is anti-correlated. Further, we show that for modulation by a white noise of amplitude $λ$ and correlation strength $F$, the system will have an extremely large response if the product of $λ^{2}F$ equals a specific combination of the frequency and the damping coefficient. This prediction can be experimentally tested. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic parametric modulation of linear and non-linear oscillators: Perturbation theory of the response function Dey, Sourin Bhattacharjee, Jayanta K. Statistical Mechanics We study a stochastically driven, damped nonlinear oscillator whose frequency is modulated by a white or coloured noise. Using diagrammatic perturbation theory, we find that in the absence of nonlinearity, parametric modulation by a coloured noise can lead to a Kapitza pendulum-like stabilization of an unstable configuration provided the noise is anti-correlated. Further, we show that for modulation by a white noise of amplitude $λ$ and correlation strength $F$, the system will have an extremely large response if the product of $λ^{2}F$ equals a specific combination of the frequency and the damping coefficient. This prediction can be experimentally tested. |
| title | Stochastic parametric modulation of linear and non-linear oscillators: Perturbation theory of the response function |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2409.01625 |