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arXiv · 2610.31408

Anisotropic spin hydrodynamics in a magnetized medium: entropy-current formulation and minimal linear modes

Yiwei Qiu·Duan She·Defu Hou
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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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Yiwei Qiu, Duan She, Defu Hou. 2026-10-22. Anisotropic spin hydrodynamics in a magnetized medium: entropy-current formulation and minimal linear modes. https://arxiv.org/abs/2610.31408

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