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Classical nonlinear response of a chaotic system: Langevin dynamics and spectral decomposition

Sergey V. Malinin·Vladimir Y. Chernyak
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Abstract

We consider the classical response of a strongly chaotic Hamiltonian system. The spectrum of such a system consists of discrete complex Ruelle-Pollicott (RP) resonances which manifest themselves in the behavior of the correlation and response functions. We interpret the RP resonances as the eigenstates and eigenvalues of the Fokker-Planck operator obtained by adding an infinitesimal noise term to the first-order Liouville operator. We demonstrate how the deterministic expression for the linear response is reproduced in the limit of vanishing noise. For the second-order response we establish an equivalence of the spectral decomposition with infinitesimal noise and the long-time asymptotic expansion for the deterministic case.

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Sergey V. Malinin, Vladimir Y. Chernyak. 2007-03-08. Classical nonlinear response of a chaotic system: Langevin dynamics and spectral decomposition. https://doi.org/10.1103/physreve.77.056202

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