The causality and stability of relativistic spin-hydrodynamics

Abstract

We study the causality and stability of relativistic hydrodynamics with the inclusion of the spin degree of freedom as a hydrodynamic field. We consider two specific models of spin-hydrodynamics for this purpose. A linear mode analysis for static background shows that a first-order dissipative spin-hydrodynamics remains acausal and admits instabilities. Besides, it is found that the inclusion of the spin field in hydrodynamics leads to new kinds of linear modes in the system. These new modes also exhibit instability and acausal behavior. The second model of the spin-hydrodynamics that we have considered here is equivalent to a particular second-order conventional hydrodynamics with no dissipative effects. For a static background, it is found that the linear modes of this model support the sound waves only. However, when the background has constant vorticity, then the model admits instability and acausality in certain situations. It is found that the spin-dynamics have an effect on the hydrodynamic response of the fluid. These findings point toward the need for a causal and stable theory with spin as a hydrodynamic field to describe the spin-polarized fluid.

arXiv comment32 pages

References in corpus (56)

• Spintronics: Fundamentals and applications
• Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid
• Chiral Magnetic and Vortical Effects in High-Energy Nuclear Collisions --- A Status Report
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• New Developments in Relativistic Viscous Hydrodynamics
• Why does the Quark-Gluon Plasma at RHIC behave as a nearly ideal fluid ?
• Relativistic fluid dynamics with spin
• Polarization of $\Lambda$ ($\bar{\Lambda }$) hyperons along the beam direction in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy
• Relativistic hydrodynamics for spin-polarized fluids
• Shear-induced spin polarization in heavy-ion collisions
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Local polarization and isothermal local equilibrium in relativistic heavy ion collisions
• Probing vorticity structure in heavy-ion collisions by local $\Lambda$ polarization
• Generating spin polarization from vorticity through nonlocal collisions
• Spin-thermal shear coupling in a relativistic fluid
• Relativistic dissipative spin dynamics in the relaxation time approximation
• Relativistic Quantum Kinetic Theory for Massive Fermions and Spin Effects
• Spin Hydrodynamics and Symmetric Energy-Momentum Tensors -- A current induced by the spin vorticity --
• Spin tensor and its role in non-equilibrium thermodynamics
• Hydrodynamics of spin currents
• Axial Kinetic Theory and Spin Transport for Fermions with Arbitrary Mass
• Non-dissipative second-order transport, spin, and pseudo-gauge transformations in hydrodynamics
• From Chiral Kinetic Theory To Relativistic Viscous Spin Hydrodynamics
• The ideal relativistic fluid limit for a medium with polarization
• The ideal relativistic spinning gas: polarization and spectra
• The ideal relativistic rotating gas as a perfect fluid with spin
• Relativistic second-order dissipative spin hydrodynamics from the method of moments
• Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics
• Effective quantum kinetic theory for spin transport of fermions with collsional effects
• A hydrodynamic study of hyperon spin polarization in relativistic heavy ion collisions
• Global and local polarization of $\Lambda$ hyperons in Au+Au collisions at 200 GeV from STAR
• Covariant Spin Kinetic Theory I: Collisionless Limit
• Causality and dissipation in relativistic polarizeable fluids
• Quantum Kinetic Theory of Spin Polarization of Massive Quarks in Perturbative QCD: Leading Log
• Ideal spin hydrodynamics from Wigner function approach
• Relativistic Spin Magnetohydrodynamics
• Relativistic hydrodynamics - causality and stability
• Hydrodynamics of simply spinning black holes & hydrodynamics for spinning quantum fluids
• Relativistic Viscous Hydrodynamics with Angular Momentum
• Spin and polarization: a new direction in relativistic heavy ion physics
• Spin polarization dynamics in the Gubser-expanding background
• Sound waves and vortices in a polarized relativistic fluid
• Thermodynamical inequivalence of quantum stress-energy and spin tensors
• Relativistic first-order spin hydrodynamics via the Chapman-Enskog expansion
• Holographic spin liquids and Lovelock Chern-Simons gravity
• Nonequilibrium Thermodynamical Inequivalence of Quantum Stress-energy and Spin Tensors
• Quark and lepton masses from top loops
• Gyrohydrodynamics: Relativistic spinful fluid with strong vorticity
• Transport and hydrodynamics in the chiral limit
• Pseudo-gauges and relativistic spin hydrodynamics for interacting Dirac and Proca fields
• Relativistic Particle and Relativistic Fluids: Magnetic Moment and Spin-Orbit Interactions
• Kubo formulae for first-order spin hydrodynamics
• Anatomy of the chiral vortical effect
• Linear mode analysis from spin transport equation
• Towards Holographic Spintronics

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• Relativistic second-order spin hydrodynamics: an entropy-current analysis
• Theories of Relativistic Dissipative Fluid Dynamics
• Hybrid approach to perfect and dissipative spin hydrodynamics
• Boost invariant spin hydrodynamics within the first order in derivative expansion
• Spin dynamics with realistic hydrodynamic background for relativistic heavy-ion collisions
• Causal and stable first-order chiral hydrodynamics
• Generalized thermodynamic relations for perfect spin hydrodynamics
• An introduction to relativistic spin hydrodynamics
• Boost-invariant spin hydrodynamics with spin feedback effects
• Analytic solutions for the linearized first-order magnetohydrodynamics and implications for causality and stability
• The evolution equation for the energy-momentum moments of the non-equilibrium density function & The regularized relativistic third order hydrodynamics
• First-order spin magnetohydrodynamics
• Anisotropic linear waves and breakdown of the momentum expansion in spin magnetohydrodynamics
• Spin hydrodynamics -- recent developments
• Hybrid framework of Fermi-Dirac spin hydrodynamics