Abstract
The dynamics of a ring of masses including dissipative forces (passive or active friction) and Toda interactions between the masses is investigated. The characteristic attractor structure and the influence of noise by coupling to a heat bath are studied. The system may be driven from the thermodynamic equilibrium to far from equilibrium states by including negative friction. We show, that over-critical pumping with free energy may lead to a partition of the phase space into attractor regions corresponding to several types of collective motions including uniform rotations, one- and multiple soliton-like excitations and relative oscillations. The distribution functions in the phase space and the correlation functions of the forces and the spectra of nonlinear excitations are calculated. We show that a finite-size Toda ring with weak thermal coupling develops at intermediate temperatures a broadband colored noise spectrum with an 1/f tail at low frequencies.
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Ebeling, W., Erdmann, U., Dunkel, J. et al. Nonlinear Dynamics and Fluctuations of Dissipative Toda Chains. Journal of Statistical Physics 101, 443–457 (2000). https://doi.org/10.1023/A:1026407415248
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DOI: https://doi.org/10.1023/A:1026407415248