Signatures of Chaos in Time Series Generated by Many-Spin Systems at High Temperatures

TL;DR

This paper introduces a new method to distinguish chaos from regular motion in many-spin systems using high-frequency tails of power spectra, supported by numerical simulations of classical and quantum spin lattices.

Contribution

The paper presents a novel approach based on analyzing higher-order derivatives and power spectra tails to identify chaos in many-particle systems, applicable to both classical and quantum models.

Findings

Chaotic spin lattices show exponential high-frequency tails in power spectra.

Nonchaotic (integrable) systems have non-exponential spectral tails.

The method's applicability limits are demonstrated with quantum spins and Toda lattice.

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 new 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.