Langevin dynamics towards Generalized Gibbs Ensembles
Abstract
In recent years, statistical physics tools have been used to study the dynamics of macroscopic quantum and classical integrable models. These studies have shown that, in the thermodynamic limit, long term time-averages of local observables equal statistical averages calculated with a Generalized Gibbs Ensemble (GGE). In the latter, the weight in phase space involves all constants of motion multiplied by Lagrange multipliers which are fixed by their initial values. We argue that the GGE can be interpreted as a proper Boltzmann measure of a different (non-standard) mechanical model. This measure can therefore be sampled with stochastic methods implemented, for example, as a Langevin process. We tailor the deterministic force in the Langevin equations so that at long times the stochastic trajectories sample the desired measure. We use the integrable Neumann Model -- the model of a classical particle constrained to move on a sphere under anisotropic harmonic potentials -- as a benchmark. We test the method in a setup where the Lagrange multipliers are fixed by the GGE governing the asymptotic dynamics of the isolated Neumann model following a quench. This problem has different phases depending on the initial conditions and quench protocol and, in all cases, with the stochastic evolution of an adequately tuned Langevin process we reproduce the asymptotic values of relevant observables.
Related
- Athermality of generalized Gibbs ensembles
- Modular Properties of W3 Generalised Gibbs Ensembles
- Modular Properties of Generalised Gibbs Ensembles: The Deformed KdV Hierarchy
- Modular properties of correlators in generalised Gibbs ensembles
- Generalised Gibbs Ensembles from the ODE/IM Correspondence: the Lee--Yang Model
BibTeX
@misc{gonzalezalbaladejo2026langevin,
title = {{Langevin dynamics towards Generalized Gibbs Ensembles}},
author = {Rafael González-Albaladejo and Leticia F. Cugliandolo and Gustavo S. Lozano and Daniel A. Stariolo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37129},
eprint = {2610.37129},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37129},
}
RIS
TY - UNPB
TI - Langevin dynamics towards Generalized Gibbs Ensembles
AU - Rafael González-Albaladejo
AU - Leticia F. Cugliandolo
AU - Gustavo S. Lozano
AU - Daniel A. Stariolo
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37129
UR - https://arxiv.org/abs/2610.37129
AB - In recent years, statistical physics tools have been used to study the dynamics of macroscopic quantum and classical integrable models. These studies have shown that, in the thermodynamic limit, long term time-averages of local observables equal statistical averages calculated with a Generalized Gibbs Ensemble (GGE). In the latter, the weight in phase space involves all constants of motion multiplied by Lagrange multipliers which are fixed by their initial values. We argue that the GGE can be interpreted as a proper Boltzmann measure of a different (non-standard) mechanical model. This measure can therefore be sampled with stochastic methods implemented, for example, as a Langevin process. We tailor the deterministic force in the Langevin equations so that at long times the stochastic trajectories sample the desired measure. We use the integrable Neumann Model -- the model of a classical particle constrained to move on a sphere under anisotropic harmonic potentials -- as a benchmark. We test the method in a setup where the Lagrange multipliers are fixed by the GGE governing the asymptotic dynamics of the isolated Neumann model following a quench. This problem has different phases depending on the initial conditions and quench protocol and, in all cases, with the stochastic evolution of an adequately tuned Langevin process we reproduce the asymptotic values of relevant observables.
ER -