Large-scale dynamics of integrable quenches
Abstract
The Ballistic Macroscopic Fluctuation Theory (BMFT) is a path-integral based approach to treat large-scale correlations in interacting integrable systems which, so far, has only been applied to quasi-equilibrium settings. In this paper we extend this approach to integrable quench problems and, to illustrate it, we compute the time evolution of the full-counting-statistics (FCS) of a conserved charge. We identify the relevant path integral, solve it via saddle-point, and obtain a set of partial differential equations describing the dynamics of the FCS. We solve these equations explicitly for free fermionic systems and for the interacting cellular automaton Rule 54. In both cases, we recover the known exact results. For Rule 54, our construction moreover completes the solution across the entire ballistic window.
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BibTeX
@misc{horvath2026largescale,
title = {{Large-scale dynamics of integrable quenches}},
author = {David X. Horvath and Bruno Bertini},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09139},
eprint = {2609.09139},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09139},
}
RIS
TY - UNPB
TI - Large-scale dynamics of integrable quenches
AU - David X. Horvath
AU - Bruno Bertini
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09139
UR - https://arxiv.org/abs/2609.09139
AB - The Ballistic Macroscopic Fluctuation Theory (BMFT) is a path-integral based approach to treat large-scale correlations in interacting integrable systems which, so far, has only been applied to quasi-equilibrium settings. In this paper we extend this approach to integrable quench problems and, to illustrate it, we compute the time evolution of the full-counting-statistics (FCS) of a conserved charge. We identify the relevant path integral, solve it via saddle-point, and obtain a set of partial differential equations describing the dynamics of the FCS. We solve these equations explicitly for free fermionic systems and for the interacting cellular automaton Rule 54. In both cases, we recover the known exact results. For Rule 54, our construction moreover completes the solution across the entire ballistic window.
ER -