Theory of Convective Diffusion
Abstract
We obtain a hydrodynamic theory of diffusive-scale dynamics in one-dimensional systems with interacting sound modes in the absence of self-interactions. Chaotic systems generically feature three distinct Gaussian relaxation processes: besides normal diffusion, driven by microscopic noise stemming from fast-decaying non-hydrodynamic modes, collisions between sound modes lead to two additional channels: convective diffusion manifesting as an effective multiplicative temporal noise, and an effective additive noise generated by the surrounding hydrodynamic modes. Our theory also includes, as a subclass, integrable systems described by generalized hydrodynamics, representing a pure realization of convective diffusion. Focusing on convective diffusion, we obtain an exact closed-form expression for the higher-point dynamical correlation functions and contrast their structure with those of normal diffusion. Additionally, we show that in convective diffusion each sound mode features a universal non-Gaussian distribution of charge transfer in its comoving frame, thereby establishing anomalous fluctuations as a characteristic feature of diffusive-scale dynamics in integrable systems.
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BibTeX
@misc{krajnik2026theory,
title = {{Theory of Convective Diffusion}},
author = {Žiga Krajnik and Takato Yoshimura and Alvise Bastianello and Enej Ilievski},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40862},
eprint = {2610.40862},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40862},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Theory of Convective Diffusion
AU - Žiga Krajnik
AU - Takato Yoshimura
AU - Alvise Bastianello
AU - Enej Ilievski
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40862
UR - https://arxiv.org/abs/2610.40862
AB - We obtain a hydrodynamic theory of diffusive-scale dynamics in one-dimensional systems with interacting sound modes in the absence of self-interactions. Chaotic systems generically feature three distinct Gaussian relaxation processes: besides normal diffusion, driven by microscopic noise stemming from fast-decaying non-hydrodynamic modes, collisions between sound modes lead to two additional channels: convective diffusion manifesting as an effective multiplicative temporal noise, and an effective additive noise generated by the surrounding hydrodynamic modes. Our theory also includes, as a subclass, integrable systems described by generalized hydrodynamics, representing a pure realization of convective diffusion. Focusing on convective diffusion, we obtain an exact closed-form expression for the higher-point dynamical correlation functions and contrast their structure with those of normal diffusion. Additionally, we show that in convective diffusion each sound mode features a universal non-Gaussian distribution of charge transfer in its comoving frame, thereby establishing anomalous fluctuations as a characteristic feature of diffusive-scale dynamics in integrable systems.
ER -