Lax dynamics

2025/04/22 by Stefano Lepri, Lepri, Stefano · 1 voice
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #nlin.SI

paper · pdf · doi:10.48550/arxiv.2504.15919

openalex publication_date 2025/04/22 · arxiv published 2025/04/22 · openalex created_date 2025/09/30 · arxiv updated 2025/10/27 · openalex updated_date 2026/08/03

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 λ_α as a proxy of the quasi-particles velocities and of the perturbed Toda actions. A set of exact equations of motion for the λ_α 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.

Discussions

• 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 therma [bsky, 1 points, 1 comments]

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