Nonlinear Fluctuating Hydrodynamics from Interacting Noisy Quantum Matter
Abstract
A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter---the boundary-driven XXZ spin chain with bulk dephasing---and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems.
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BibTeX
@misc{christopoulos2026nonlinear,
title = {{Nonlinear Fluctuating Hydrodynamics from Interacting Noisy Quantum Matter}},
author = {Alexios Christopoulos and João Costa and Stefano Scopa and Jacopo De Nardis and Zala Lenarčič and Denis Bernard and Tony Jin},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2609.00159},
eprint = {2609.00159},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00159},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Nonlinear Fluctuating Hydrodynamics from Interacting Noisy Quantum Matter
AU - Alexios Christopoulos
AU - João Costa
AU - Stefano Scopa
AU - Jacopo De Nardis
AU - Zala Lenarčič
AU - Denis Bernard
AU - Tony Jin
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2609.00159
UR - https://arxiv.org/abs/2609.00159
AB - A universal characterization of non-equilibrium steady states in interacting quantum many-body systems remains one of the central challenges of statistical physics. Here, we address this problem for a paradigmatic model of diffusive interacting quantum matter---the boundary-driven XXZ spin chain with bulk dephasing---and derive, directly from its microscopic Lindblad dynamics, an emergent classical Macroscopic Fluctuation Theory (MFT) governing its large-scale fluctuations. Crucially, the resulting hydrodynamics carries a density-dependent diffusivity and mobility as the fingerprint of interactions. This effective description enables the exact computation of the stationary density profile, long-range correlations, and the full counting statistics of the current, in excellent agreement with tensor-network simulations. Our work demonstrates that noisy quantum many-body systems can realize the universality class of genuinely interacting diffusive matter, beyond the constant-diffusivity class of the symmetric simple exclusion process, and establishes MFT as a powerful universal framework for interacting diffusive quantum systems.
ER -