Malishava M, Flach S. Lyapunov Spectrum Scaling for Classical Many-Body Dynamics Close to Integrability.
PHYSICAL REVIEW LETTERS 2022;
128:134102. [PMID:
35426693 DOI:
10.1103/physrevlett.128.134102]
[Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2021] [Revised: 12/02/2021] [Accepted: 03/08/2022] [Indexed: 05/29/2023]
Abstract
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.
Collapse