Effective field theories of nonlinear fluctuating hydrodynamics in one dimension

Matija Koterle; Enej Ilievski

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arXiv · 2607.22527

Effective field theories of nonlinear fluctuating hydrodynamics in one dimension

Matija Koterle·Enej Ilievski

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Abstract

Describing emergent macroscopic phenomena in low spatial dimensions is known to be notoriously challenging, primarily due to strong interactions that render perturbative approaches inapplicable. On the other hand, low-dimensional systems host a wealth of unorthodox phenomena. A prominent example is the emergence of superdiffusive transport in one-dimensional interacting systems, traditionally studied in the framework of nonlinear fluctuating hydrodynamics. After identifying and discussing internal inconsistencies in the previous formulations, in this work we develop a general and systematic approach for constructing effective field theories of one-dimensional hydrodynamic systems in the form of coupled stochastic Langevin-type equations compatible with the physical requirements of local equilibrium states such as the thermodynamic Maxwell relation and fluctuation-dissipation symmetry. We implemented a general numerical integration scheme and exemplified our construction on a simple model of two interacting hydrodynamic modes with a non-Gaussian stationary equilibrium measure.

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Matija Koterle, Enej Ilievski. 2026-07-24. Effective field theories of nonlinear fluctuating hydrodynamics in one dimension. https://arxiv.org/abs/2607.22527

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