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Lyapunov Spectrum Scaling for Classical Many-Body Dynamics Close to Integrability

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Title
Lyapunov Spectrum Scaling for Classical Many-Body Dynamics Close to Integrability
Author(s)
Merab Malishava; Sergej Flach
Publication Date
2022-03
Journal
Physical Review Letters, v.128, no.13
Publisher
American Physical Society
Abstract
© 2022 American Physical Society.We propose a novel framework to characterize the thermalization of many-body dynamical systems close to integrable limits using the scaling properties of the full Lyapunov spectrum. We use a classical unitary map model to investigate macroscopic weakly nonintegrable dynamics beyond the limits set by the KAM regime. We perform our analysis in two fundamentally distinct long-range and short-range integrable limits which stem from the type of nonintegrable perturbations. Long-range limits result in a single parameter scaling of the Lyapunov spectrum, with the inverse largest Lyapunov exponent being the only diverging control parameter and the rescaled spectrum approaching an analytical function. Short-range limits result in a dramatic slowing down of thermalization which manifests through the rescaled Lyapunov spectrum approaching a non-analytic function. An additional diverging length scale controls the exponential suppression of all Lyapunov exponents relative to the largest one.
URI
https://pr.ibs.re.kr/handle/8788114/11435
DOI
10.1103/PhysRevLett.128.134102
ISSN
0031-9007
Appears in Collections:
Center for Theoretical Physics of Complex Systems(복잡계 이론물리 연구단) > 1. Journal Papers (저널논문)
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