Odd stochastic density functional theory
Abstract
Stochastic density functional theory (SDFT) provides a powerful framework for studying the dynamics of many-body systems both in and out of equilibrium. In its standard form, it can be viewed as a density-based formulation of coupled Langevin equations with white noise. Here, we extend SDFT to a class of systems, ranging from magnetized electrolytes to chiral active matter, that possess a chiral overdamped limit in which a relaxation timescale and an oscillation period are simultaneously taken to zero. We derive this formulation, which we dub ``odd SDFT", by taking the overdamped limit of a fluctuating hydrodynamic description of underdamped particles subject to a Lorentz force. We establish the validity and utility of the resulting framework by calculating the collective mobility tensor of interacting particles using both direct linear response and a Green-Kubo relation. We then apply the theory to the Hall conductivity of electrolytes in magnetic fields. Going beyond mean-field theory and using two distinct Green-Kubo relations, we derive the full conductivity tensor, extending the relaxation part of the Debye-Hückel-Onsager theory to the case of finite magnetic fields.
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BibTeX
@misc{avni2026stochastic,
title = {{Odd stochastic density functional theory}},
author = {Yael Avni and Michel Fruchart and David Martin and Tali Khain and Vincenzo Vitelli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.32080},
eprint = {2609.32080},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32080},
}
RIS
TY - UNPB
TI - Odd stochastic density functional theory
AU - Yael Avni
AU - Michel Fruchart
AU - David Martin
AU - Tali Khain
AU - Vincenzo Vitelli
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2609.32080
UR - https://arxiv.org/abs/2609.32080
AB - Stochastic density functional theory (SDFT) provides a powerful framework for studying the dynamics of many-body systems both in and out of equilibrium. In its standard form, it can be viewed as a density-based formulation of coupled Langevin equations with white noise. Here, we extend SDFT to a class of systems, ranging from magnetized electrolytes to chiral active matter, that possess a chiral overdamped limit in which a relaxation timescale and an oscillation period are simultaneously taken to zero. We derive this formulation, which we dub ``odd SDFT", by taking the overdamped limit of a fluctuating hydrodynamic description of underdamped particles subject to a Lorentz force. We establish the validity and utility of the resulting framework by calculating the collective mobility tensor of interacting particles using both direct linear response and a Green-Kubo relation. We then apply the theory to the Hall conductivity of electrolytes in magnetic fields. Going beyond mean-field theory and using two distinct Green-Kubo relations, we derive the full conductivity tensor, extending the relaxation part of the Debye-Hückel-Onsager theory to the case of finite magnetic fields.
ER -