Classical nonlinear response of a chaotic system: Langevin dynamics and spectral decomposition
arXiv:nlin/0703014 · doi:10.1103/PhysRevE.77.056202
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.
16 pages, 1 figure
References in corpus (6)
- Resonances of the Frobenius-Perron Operator for a Hamiltonian Map with a Mixed Phase Space
- Relaxation to the Invariant Density for Kicked Rotor
- Spectral properties of noisy classical and quantum propagators
- The leading Ruelle resonances of chaotic maps
- Classical nonlinear response of a chaotic system: collective resonances
- Spectral Decompositions for Evolution Opertors of Mixing Dynamical Systems