Anisotropic spin hydrodynamics in a magnetized medium: entropy-current formulation and minimal linear modes
Abstract
We formulate anisotropic relativistic spin hydrodynamics in a parity-even magnetized medium using an Israel--Stewart entropy-current construction. Treating the magnetic field at leading order in the gradient expansion reduces the rotational symmetry to SO(2) and separates spin susceptibilities and dissipative transport into longitudinal, transverse, and mixed channels. A restricted quadratic entropy current yields transient equations for the retained dissipative stresses and spin fluxes. We analyze a minimal linear closure around an unpolarized homogeneous equilibrium, retaining dynamical magnetic-flux perturbations but no explicit spin-magnetization coupling; spin and magnetic fluctuations mix through the fluid variables. Infrared coefficient equations and ultraviolet characteristic expansions organize the magnetosonic and Alfvén-like spectra together with spectator spin-flux poles. The first-order truncation exhibits unstable boost-sector poles and superlinear large-wave-number branches, interpreted as diagnostics of the truncated equations rather than microscopic dispersion predictions. For the baseline parameters, finite relaxation times yield asymptotically linear propagation branches and finite relaxation poles, with no growing modes found on the sampled grid. The characteristic speeds depend nonmonotonically on spin transport and provide necessary light-cone diagnostics, without establishing general stability or strong hyperbolicity.
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BibTeX
@misc{qiu2026anisotropic,
title = {{Anisotropic spin hydrodynamics in a magnetized medium: entropy-current formulation and minimal linear modes}},
author = {Yiwei Qiu and Duan She and Defu Hou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31408},
eprint = {2610.31408},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31408},
}
RIS
TY - UNPB
TI - Anisotropic spin hydrodynamics in a magnetized medium: entropy-current formulation and minimal linear modes
AU - Yiwei Qiu
AU - Duan She
AU - Defu Hou
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31408
UR - https://arxiv.org/abs/2610.31408
AB - We formulate anisotropic relativistic spin hydrodynamics in a parity-even magnetized medium using an Israel--Stewart entropy-current construction. Treating the magnetic field at leading order in the gradient expansion reduces the rotational symmetry to SO(2) and separates spin susceptibilities and dissipative transport into longitudinal, transverse, and mixed channels. A restricted quadratic entropy current yields transient equations for the retained dissipative stresses and spin fluxes. We analyze a minimal linear closure around an unpolarized homogeneous equilibrium, retaining dynamical magnetic-flux perturbations but no explicit spin-magnetization coupling; spin and magnetic fluctuations mix through the fluid variables. Infrared coefficient equations and ultraviolet characteristic expansions organize the magnetosonic and Alfvén-like spectra together with spectator spin-flux poles. The first-order truncation exhibits unstable boost-sector poles and superlinear large-wave-number branches, interpreted as diagnostics of the truncated equations rather than microscopic dispersion predictions. For the baseline parameters, finite relaxation times yield asymptotically linear propagation branches and finite relaxation poles, with no growing modes found on the sampled grid. The characteristic speeds depend nonmonotonically on spin transport and provide necessary light-cone diagnostics, without establishing general stability or strong hyperbolicity.
ER -