Lax dynamics
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911232682885120 |
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| author | Lepri, Stefano |
| author_facet | Lepri, Stefano |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15919 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lax dynamics Lepri, Stefano Exactly Solvable and Integrable Systems Statistical Mechanics 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. |
| title | Lax dynamics |
| topic | Exactly Solvable and Integrable Systems Statistical Mechanics |
| url | https://arxiv.org/abs/2504.15919 |