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Register a new userKinetic approach to polarization-vorticity coupling and hydrodynamics with spin
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Authors
Avdhesh Kumar
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Recently introduced equilibrium Wigner functions for spin-one-half particles are used in the semiclassical kinetic equations to study the relation between spin polarization and vorticity. It is found, in particular, that such a framework does not necessarily imply that the thermal-vorticity and spin polarization tensors are equal. Subsequently, a procedure to formulate the hydrodynamic framework for particles with spin-one-half, based on the semiclassical expansion, is outlined.
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Newly introduced equilibrium Wigner functions for particles with spin one-half are used in the semi-classical kinetic equations to study a possible relation between thermal vorticity and spin polarization. It is shown that in global equilibrium both the thermal-vorticity and spin polarization tensors are constant but not necessarily equal. In the case of local equilibrium, we define a procedure leading to hydrodynamic equations with spin. We introduce such equations for the de~Groot, van~Leeuwen, and van~Weert (GLW) formalism as well as for the canonical scheme (these two frameworks differ by the definitions of the energy-momentum and spin tensors). It is found that the GLW and canonica
The hot and dense matter generated in heavy-ion collisions contains intricate vortical structure in which the local fluid vorticity can be very large. Such vorticity can polarize the spin of the produced particles. We study the event-by-event generation of the so-called thermal vorticity in Au + Au collisions at energy region $sqrt{s}=7.7-200$ GeV and calculate its time evolution, spatial distribution, etc., in a multiphase transport (AMPT) model. We then compute the spin polarization of the $Lambda$ and $bar{Lambda}$ hyperons as a function of $sqrt{s}$, transverse momentum $p_T$, rapidity, and azimuthal angle. Furthermore, we study the harmonic flow of the spin, in a manner analogous to the harmonic flow of the particle number. The measurement of the spin harmonic flow may provide a way to probe the vortical structure in heavy-ion collisions. We also discuss the spin polarization of $Xi^0$ and $Omega^-$ hyperons which may provide further information about the spin polarization mechanism of hadrons.
A global equilibrium state of a spin polarized fluid that undergoes constant acceleration along the stream lines is described as a solution of recently introduced perfect-fluid hydrodynamic equations with spin 1/2.
A newly proposed framework of perfect-fluid relativistic hydrodynamics for particles with spin 1/2 is briefly reviewed. The hydrodynamic equations follow entirely from the conservation laws for energy, momentum, and angular momentum. The incorporation of the angular-momentum conservation requires that the spin polarization tensor is introduced. It plays a role of a Lagrange multiplier conjugated to the spin tensor. The space-time evolution of the spin polarization tensor depends on the specific form chosen for the spin tensor.
We review studies of vortical motion and the resulting global polarization of $Lambda$ and $bar{Lambda}$ hyperons in heavy-ion collisions, in particular, within 3FD model. 3FD predictions for the global midrapidity polarization in the FAIR-NICA energy range are presented. The 3FD simulations indicate that energy dependence of the observed global polarization of hyperons in the midrapidity region is a consequence of the decrease of the vorticity in the central region with the collision energy rise because of pushing out the vorticity field into the fragmentation regions. At high collision energies this pushing-out results in a peculiar vortical structure consisting of two vortex rings: one ring in the target fragmentation region and another one in the projectile fragmentation region with matter rotation being opposite in these two rings.
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