title: Signatures of chaos in time series generated by many-spin systems at high temperatures.
abstract: Extracting reliable indicators of chaos from a single experimental time series is a challenging task, in particular, for systems with many degrees of freedom. The techniques available for this purpose often require unachievably long time series. In this paper, we explore a method of discriminating chaotic from multi-periodic integrable motion in many-particle systems. The applicability of this method is supported by our numerical simulations of the dynamics of classical spin lattices at high temperatures. We compared chaotic and nonchaotic regimes of these lattices and investigated the transition between the two. The method is based on analyzing higher-order time derivatives of the time series of a macroscopic observable-the total magnetization of the spin lattice. We exploit the fact that power spectra of the magnetization time series generated by chaotic spin lattices exhibit exponential high-frequency tails, while, for the integrable spin lattices, the power spectra are terminated in a non-exponential way. We have also demonstrated the applicability limits of the above method by investigating the high-frequency tails of the power spectra generated by quantum spin lattices and by the classical Toda lattice.
authors.affiliation: Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany.
authors.forename: Tarek A
authors.initials: TA
authors.lastname: Elsayed
authors.affiliation: Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Hess
authors.affiliation: Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany and Department of Physics, School of Science and Technology, Nazarbayev University, 53 Kabanbai Batyr Ave., Astana 010000, Kazakhstan and Skolkovo Institute of Science and Technology, 100 Novaya Str., Skolkovo, Moscow Region 143025, Russia.
authors.forename: Boris V
authors.initials: BV
authors.lastname: Fine
mesh_terms: D003198:Computer Simulation; D055590:Electromagnetic Phenomena; D019277:Entropy; D009038:Motion; D017711:Nonlinear Dynamics; D013696:Temperature; D013997:Time Factors