| Issue |
EPL
Volume 152, Number 3, November 2025
|
|
|---|---|---|
| Article Number | 33002 | |
| Number of page(s) | 6 | |
| Section | Fluid and nonlinear dynamics | |
| DOI | https://doi.org/10.1209/0295-5075/ae1638 | |
| Published online | 10 November 2025 | |
Lax dynamics
Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi - via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Firenze - via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
Received: 11 September 2025
Accepted: 22 October 2025
Abstract
A novel approach is proposed to characterize the dynamics of perturbed many-body integrable systems. Focusing on the paradigmatic case of the Toda chain under non-integrable Hamiltonian perturbations, this study introduces a method based the time evolution of the Lax eigenvalues 
as a proxy of the quasi-particles velocities and of the perturbed Toda actions. A set of exact equations of motion for the is derived that closely resemble those for eigenenergies of a quantum problem (also known as the Pechukas-Yukawa gas). Numerical simulations suggest that the invariant measure of such dynamics is basically the thermal density of states of the Toda lattice, regardless of the form of the perturbation.
© 2025 The author(s)
Published by the EPLA under the terms of the Creative Commons Attribution 4.0 International License (CC-BY). Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.