Generating spin polarization from vorticity through nonlocal collisions

Abstract

We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in $\hslash$ it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudo-gauge the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes only in global equilibrium and that the spin potential is then equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.

arXiv comment7 pages

References in corpus (63)

• Global $\Lambda$ hyperon polarization in nuclear collisions: evidence for the most vortical fluid
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Globally Polarized Quark-gluon Plasma in Non-central A+A Collisions
• Angular momentum conservation in heavy ion collisions at very high energy
• The angular momentum controversy: What's it all about and does it matter?
• 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
• Kinetic theory with Berry curvature from quantum field theories
• Global hyperon polarization at local thermodynamic equilibrium with vorticity, magnetic field and feed-down
• 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
• Polarization probes of vorticity in heavy ion collisions
• A study of vorticity formation in high energy nuclear collisions
• Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy
• Polarization and Vorticity in the Quark Gluon Plasma
• Kinetic theory for massive spin-1/2 particles from the Wigner-function formalism
• Relativistic hydrodynamics for spin-polarized fluids
• Vortical fluid and $\Lambda$ spin correlations in high-energy heavy-ion collisions
• Lambda Polarization in Peripheral Heavy Ion Collisions
• Polarization of massive fermions in a vortical fluid
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Relativistic Chiral Kinetic Theory from Quantum Field Theories
• Evidence of spin-orbital angular momentum interactions in relativistic heavy-ion collisions
• Collisions in Chiral Kinetic Theory
• Global $\Lambda$ Polarization in high energy collisions
• Nonlinear Responses of Chiral Fluids from Kinetic Theory
• Relativistic dissipative spin dynamics in the relaxation time approximation
• Relativistic Quantum Kinetic Theory for Massive Fermions and Spin Effects
• Spin tensor and its role in non-equilibrium thermodynamics
• Complete and Consistent Chiral Transport from Wigner Function Formalism
• Axial Kinetic Theory and Spin Transport for Fermions with Arbitrary Mass
• Spin-dependent distribution functions for relativistic hydrodynamics of spin-1/2 particles
• The ideal relativistic fluid limit for a medium with polarization
• Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory
• Thermodynamic versus kinetic approach to polarization-vorticity coupling
• Scalar quantum kinetic theory for spin-1/2 particles: mean field theory
• Covariant statistical mechanics and the stress-energy tensor
• Local spin polarization in high energy heavy ion collisions
• Mass Correction to Chiral Kinetic Equations
• Effective quantum kinetic theory for spin transport of fermions with collsional effects
• Spin polarization evolution in a boost invariant hydrodynamical background
• Spin Polarizations in a Covariant Angular-Momentum-Conserved Chiral Transport Model
• Covariant Spin Kinetic Theory I: Collisionless Limit
• Feed-down effect on $\Lambda$ spin polarization
• Linear response theory of relativistic hydrodynamics with spin
• Longitudinal spin polarization in a thermal model
• Causality and dissipation in relativistic polarizeable fluids
• Disentangling covariant Wigner functions for chiral fermions
• Quantum Kinetic Theory of Spin Polarization of Massive Quarks in Perturbative QCD: Leading Log
• Polarization transfer in hyperon decays and its effect in relativistic nuclear collisions
• Sound waves and vortices in a polarized relativistic fluid
• Azimuthal angle dependence of the longitudinal spin polarization in relativistic heavy ion collisions
• A microscopic description for polarization in particle scatterings
• Perfect-fluid hydrodynamics with constant acceleration along the stream lines and spin polarization
• Side-Jump Induced Spin-Orbit Interaction of Chiral Fluids from Kinetic Theory
• Consistent Relativistic Chiral Kinetic Theory: a derivation from OSEFT
• The chiral vortical effect in Wigner function approach
• Fully relativistic kinetic equation for spin-1/2 particles in the long scale-length approximation
• Retarded versus time-nonlocal quantum kinetic equations
• Relativistic kinetic theory for spin-1/2 particles: Conservation laws, thermodynamics, and linear waves
• Nonequilibrium thermodynamics with binary quantum correlations
• Correlational latent heat by nonlocal quantum kinetic theory

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• Relativistic dissipative spin dynamics in the relaxation time approximation
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• Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory
• Dissipative Spin Dynamics in Relativistic Matter
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• From Kadanoff--Baym to Boltzmann equations for massive spin-1/2 fermions
• Reexamination of local spin polarization beyond global equilibrium in relativistic heavy ion collisions
• Spin alignment of vector mesons in heavy-ion collisions
• Foundations and Applications of Quantum Kinetic Theory
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• The Present and Future of QCD
• Spin polarization dynamics in the Gubser-expanding background
• Relativistic Viscous Hydrodynamics with Angular Momentum
• Analytic solutions of relativistic dissipative spin hydrodynamics with Bjorken expansion
• Relativistic dissipative spin hydrodynamics from kinetic theory with a nonlocal collision term
• Relativistic second-order spin hydrodynamics: an entropy-current analysis
• Theories of Relativistic Dissipative Fluid Dynamics
• Local and global polarization of $\Lambda$ hyperons across RHIC-BES energies: the roles of spin hall effect, initial condition and baryon diffusion
• Relativistic first-order spin hydrodynamics via the Chapman-Enskog expansion
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• Vorticity and Spin Polarization in Heavy Ion Collisions: Transport Models
• Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: scalar field
• Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field
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• Pseudogauge dependence of the spin polarization and of the axial vortical effect
• Pseudo-gauges and relativistic spin hydrodynamics for interacting Dirac and Proca fields
• Quantum kinetic theory for dynamical spin polarization from QED-type interaction
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• Spin Polarization Formula for Dirac Fermions at Local Equilibrium
• Effect of thermal shear on longitudinal spin polarization in a thermal model
• Spin polarization dynamics in the non-boost-invariant background
• Spin relaxation rate for heavy quarks in weakly coupled QCD plasma
• Stability studies of first order spin-hydrodynamic frameworks
• The causality and stability of relativistic spin-hydrodynamics
• Global polarization effect and spin-orbit coupling in strong interaction
• Lorentz-covariant nonlocal collision term for spin-1/2 particles
• Dynamics of Hot QCD Matter -- Current Status and Developments
• Analytic solutions of relativistic dissipative spin hydrodynamics with radial expansion in Gubser flow
• Hydrodynamic helicity polarization in relativistic heavy ion collisions
• Spin alignment of vector mesons by second-order hydrodynamic gradients
• Damping of spin waves
• Global spin polarization of multistrange hyperons and feed-down effect in heavy-ion collisions
• Relativistic hydrodynamics with spin in the presence of electromagnetic fields
• Spin polarization and correlation of quarks from glasma
• Shear induced polarization: Collisional contributions
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• Spin evolution of massive fermion in QED plasma
• Hybrid approach to perfect and dissipative spin hydrodynamics
• Quantum kinetic theory for spin transport of quarks with background chromo-electromagnetic fields
• Boost invariant spin hydrodynamics within the first order in derivative expansion
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• Lorentz-covariant kinetic theory for massive spin-1/2 particles
• Linear mode analysis from spin transport equation
• Resummed spin hydrodynamics from quantum kinetic theory
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• Photoproduction of $e^{+}{e}^{-}$ in peripheral isobar collisions
• Linear response hydrodynamics of a relativistic dissipative fluid with spin
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• Transverse and longitudinal spin alignment from color fields in heavy ion collisions
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• Evolution of global polarization in relativistic heavy-ion collisions within a perturbative approach
• Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions
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• Application range of perfect spin hydrodynamics
• Estimating Longitudinal Polarization of $\Lambda$ and $\bar{\Lambda }$ Hyperons at Relativistic Energies using Hydrodynamic and Transport models
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• On kinetic theories with color and spin from amplitudes
• Polarization in heavy ion collisions: a theoretical review
• Lepton pair production in ultra-peripheral collisions
• Perfect spin hydrodynamics at all orders in spin polarization
• Spin Boltzmann equation for non-relativistic spin-1/2 fermions
• On the non-uniqueness of the energy-momentum and spin currents
• In-medium Electromagnetic Form Factors and Spin Polarizations
• Anomalous spin polarization from turbulent color fields
• Minimal-Length Corrections to Hyperon Polarization in Rotating Quark Gluon Plasma
• Study of spin polarization dependence on rapidity, transverse momentum, and azimuthal angle
• Dissipative effects on the propagation of spin modes
• A topological realization of spin polarization through vortex formation in collisions of Bose-Einstein condensates
• Guiding center hydrodynamics with spin
• Perfect spinfluid: A divergence-type approach
• Impact of spin polarization on transport and thermodynamic coefficients
• Nonlinear causality and stability of perfect spin hydrodynamics and its nonperturbative character
• Theoretical aspects of relativistic spin hydrodynamics coupled with electromagnetic fields