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 space-time gradient 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 in space-time gradient.

Equivalence of canonical and phenomenological formulations of spin hydrodynamics

“…The canonical framework uses the energy-momentum tensor, which contains both symmetric and antisymmetric parts, and the canonical spin tensor is totally antisymmetric. The latter property follows directly from a microscopic theory [28], but does not provide a natural identification of the tensor S µν in Eq. ( 4) as the spin density.…”

“…Recent observations of spin polarization of weakly decaying hyperons produced in relativistic heavy-ion experiments across various collision energies [1][2][3][4][5][6][7][8][9] have provided a unique probe to study polarization phenomena in relativistic nuclear matter under rotation [10]. Motivated by the earlier successes of relativistic fluid dynamics in heavy-ion phenomenology [11], several extensions of relativistic hydrodynamics for the spinpolarized fluids have been developed using quantum statistical density operators [12][13][14][15][16], relativistic kinetic theory [17][18][19][20][21][22][23][24][25][26][27][28][29], effective Lagrangian approach [30][31][32][33], entropy current analysis [34][35][36][37][38][39], holography [40,41] and equilibrium partition functions [42].…”

“…Last but not least, at the microscopic level, the canonical forms of conserved currents with the energy-momentum tensor having both symmetric and antisymmetric parts and the spin tensor being totally antisymmetric in all its Lorentz indices, can be obtained. Such a choice of conserved currents is motivated from the standpoint of the quantum field theory of Dirac fermions when applying the Noether theorem [28].…”

Spin Polarization Formula for Dirac Fermions at Local Equilibrium

“…Possible resolutions have been proposed including admitting different spin potentials (see definition below) to govern the amount of spin polarization [26,27], assuming strong chiral anomaly effects [31], and so on. New theoretical tools like spin kinetic theory [11,[38][39][40][41][42][43][44][45][46][47][48][49] and spin hydrodynamics [50][51][52][53][54][55][56][57][58][59][60][61][62][63][64][65] that can be used to study the spin polarization out of global equilibrium are also under development though no numerical results have been obtained so far.…”

Relativistic spin hydrodynamics with torsion and linear response theory for spin relaxation

“…However, the recent experimental observation of spin polarization of hadrons in relativistic heavy-ion collisions [7][8][9][10] strongly motivates the development of the theory describing spin transport in relativistic plasma, in particular, the quark-gluon plasma (QGP). This motivation has led to several theoretical studies of relativistic hydrodynamics with spin polarization, based on the second law of thermodynamics [11][12][13][14][15], equilibrium partition functions [15], quantum kinetic theory of relativistic fermions [16][17][18][19][20][21][22][23][24][25], holographic approach for strongly-coupled plasma [26][27][28], effective Lagrangian approach [29][30][31], and quantum statistical density operators [32][33][34][35][36] (see also Refs. [37][38][39] and references therein for a review).…”