Hall conductance of dilute electrolytes from odd stochastic density functional theory
Abstract
Electrolytes under an external magnetic field exhibit a Hall conductivity, much like metals and semiconductors. However, existing theories fail to quantitatively account for their measured Hall conductivities. To make progress toward such a theory, we develop a stochastic density functional framework for electrolytes in a magnetic field. This framework, which we dub odd SDFT, extends the celebrated stochastic density functional theory (SDFT) to incorporate transverse mobilities and chiral time-correlated noise. Using this framework, we calculate the Hall conductivity in the absence of hydrodynamic solvent effects through three approaches: (i) direct response, (ii) Green-Kubo relation, and (iii) a hybrid fluctuation-dissipation relation. We further show that odd SDFT applies more broadly to fluids with broken time-reversal and mirror symmetry, including odd-diffusive fluids and chiral active matter. Our results generalize the relaxation correction of Debye-Hückel-Onsager theory to magnetized electrolytes and provide a foundation for incorporating additional effects mediated by the solvent that could quantitatively reconcile theory and experiments.
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BibTeX
@misc{avni2026hall,
title = {{Hall conductance of dilute electrolytes from 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.2609.33797},
eprint = {2609.33797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33797},
}
RIS
TY - UNPB
TI - Hall conductance of dilute electrolytes from 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.2609.33797
UR - https://arxiv.org/abs/2609.33797
AB - Electrolytes under an external magnetic field exhibit a Hall conductivity, much like metals and semiconductors. However, existing theories fail to quantitatively account for their measured Hall conductivities. To make progress toward such a theory, we develop a stochastic density functional framework for electrolytes in a magnetic field. This framework, which we dub odd SDFT, extends the celebrated stochastic density functional theory (SDFT) to incorporate transverse mobilities and chiral time-correlated noise. Using this framework, we calculate the Hall conductivity in the absence of hydrodynamic solvent effects through three approaches: (i) direct response, (ii) Green-Kubo relation, and (iii) a hybrid fluctuation-dissipation relation. We further show that odd SDFT applies more broadly to fluids with broken time-reversal and mirror symmetry, including odd-diffusive fluids and chiral active matter. Our results generalize the relaxation correction of Debye-Hückel-Onsager theory to magnetized electrolytes and provide a foundation for incorporating additional effects mediated by the solvent that could quantitatively reconcile theory and experiments.
ER -