Ideal spin hydrodynamics from Wigner function approach

Abstract

Based on the Wigner function in local equilibrium, we derive hydrodynamical quantities for a system of polarized spin-1/2 particles: the particle number current density, the energy-momentum tensor, the spin tensor, and the dipole moment tensor. Comparing with ideal hydrodynamics without spin, additional terms at first and second order in the Knudsen number $\text{Kn}$ and the average spin polarization ${\chi }_s$ have been derived. The Wigner function can be expressed in terms of matrix-valued distributions, whose equilibrium forms are characterized by thermodynamical parameters in quantum statistics. The equations of motions for these parameters are derived by conservation laws at the leading and next-to-leading order $\text{Kn}$ and ${\chi }_s$.

arXiv comment8 pages, no figure

References in corpus (45)

• The Chiral Magnetic Effect
• The effects of topological charge change in heavy ion collisions: "Event by event P and CP violation"
• Collective flow and viscosity in relativistic heavy-ion collisions
• Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid
• Hydrodynamic Modeling of Heavy-Ion Collisions
• Parity violation in hot QCD: why it can happen, and how to look for it
• New Developments in Relativistic Viscous Hydrodynamics
• Globally Polarized Quark-gluon Plasma in Non-central A+A Collisions
• Angular momentum conservation in heavy ion collisions at very high energy
• Relativistic distribution function for particles with spin at local thermodynamical equilibrium
• Global polarization of $\Lambda$ hyperons in Au+Au collisions at $\sqrt{s_{{}_{NN}}}$ = 200 GeV
• Relativistic fluid dynamics with spin
• Study of Lambda polarization in relativistic nuclear collisions at sqrt{s}_NN = 7.7-200 GeV
• 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
• Global $\Lambda$ polarization in heavy-ion collisions from a transport model
• Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism
• Relativistic hydrodynamics for spin-polarized fluids
• Lambda Polarization in Peripheral Heavy Ion Collisions
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Thermal vorticity and spin polarization in heavy-ion collisions
• Global $\Lambda$ Polarization in high energy collisions
• Lambda hyperon polarization in relativistic heavy ion collisions from the chiral kinetic approach
• Testing the Chiral Magnetic Effect with Central U+U collisions
• 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 --
• Axial Kinetic Theory and Spin Transport for Fermions with Arbitrary Mass
• Non-dissipative second-order transport, spin, and pseudo-gauge transformations in hydrodynamics
• The ideal relativistic fluid limit for a medium with polarization
• Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles
• Anomalous chiral transports and spin polarization in heavy-ion collisions
• Dissipative Spin Dynamics in Relativistic Matter
• The ideal relativistic rotating gas as a perfect fluid with spin
• Local spin polarization in high energy heavy ion collisions
• Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics
• Mass Correction to Chiral Kinetic Equations
• Longitudinal spin polarization in a thermal model
• Quantum Kinetic Theory of Spin Polarization of Massive Quarks in Perturbative QCD: Leading Log
• Sound waves and vortices in a polarized relativistic fluid
• Nonequilibrium Thermodynamical Inequivalence of Quantum Stress-energy and Spin Tensors
• Quantum kinetic theory for spin-1/2 fermions in Wigner function formalism
• Kinetic theory with spin: From massive to massless fermions
• Relaxation Times for Chiral Transport Phenomena and Spin Polarization in Strongly Coupled Plasma
• Hydrodynamics with spin --- recent developments

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• Lambda polarization in ${}^{108}$Ag +${}^{108}$Ag and ${}^{197}$Au +${}^{197}$Au collisions around a few GeV
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