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Register a new userRelativistic dissipative spin dynamics in the relaxation time approximation
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The concept of the Wigner function is used to construct a semi-classical kinetic theory describing the evolution of the axial-current phase-space density of spin-1/2 particles in the relaxation time approximation. The resulting approach can be used to study spin-polarization effects in relativistic matter, in particular, in heavy-ion collisions. An expression for the axial current based on the classical treatment of spin is also introduced and we show that it is consistent with earlier calculations using Wigner functions. Finally, we derive non-equilibrium corrections to the spin tensor, which are used to define, for the first time, the structure of spin transport coefficients in relativistic matter.
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Here we derive the relativistic resistive dissipative second-order magnetohydrodynamic evolution equations using the Boltzmann equation, thus extending our work from the previous paper href{https://link.springer.com/article/10.1007/JHEP03(2021)216}{JHEP 03 (2021) 216} where we considered the non-resistive limit. We solve the Boltzmann equation for a system of particles and antiparticles using the relaxation time approximation and the Chapman-Enskog like gradient expansion for the off-equilibrium distribution function, truncating beyond second-order. In the first order, the bulk and shear stress are independent of the electromagnetic field, however, the diffusion current, shows a dependence on the electric field. In the first order, the transport coefficients~(shear and bulk stress) are shown to be independent of the electromagnetic field. The diffusion current, however, shows a dependence on the electric field. In the second-order, the new transport coefficients that couple electromagnetic field with the dissipative quantities appear, which are different from those obtained in the 14-moment approximation~cite{Denicol:2019iyh} in the presence of the electromagnetic field. Also we found out the various components of conductivity in this case.
In this work, we briefly review the progress made in the formulation of hydrodynamics with spin with emphasis on the application to the relativistic heavy-ion collisions. In particular, we discuss the formulation of hydrodynamics with spin for perfect-fluid and the first order viscous corrections with some discussion on the calculation of spin kinetic coefficients. Finally, we apply relativistic hydrodynamics with spin to the relativistic heavy-ion collisions to calculate the spin polarization of $Lambda$-particles.
The stability and causality of the Landau-Lifshitz theory and the Israel-Stewart type causal dissipative hydrodynamics are discussed. We show that the problem of acausality and instability are correlated in relativistic dissipative hydrodynamics and instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.
The microscopic formulae of the bulk viscosity $zeta $ and the corresponding relaxation time $tau_{Pi}$ in causal dissipative relativistic fluid dynamics are derived by using the projection operator method. In applying these formulae to the pionic fluid, we find that the renormalizable energy-momentum tensor should be employed to obtain consistent results. In the leading order approximation in the chiral perturbation theory, the relaxation time is enhanced near the QCD phase transition and $tau_{Pi}$ and $zeta $ are related as $tau_{Pi}=zeta /[beta {(1/3-c_{s}^{2})(epsilon +P)-2(epsilon -3P)/9}]$, where $epsilon $, $P$ and $c_{s}$ are the energy density, pressure and velocity of sound, respectively. The predicted $zeta $ and $% tau_{Pi}$ should satisfy the so-called causality condition. We compare our result with the results of the kinetic calculation by Israel and Stewart and the string theory, and confirm that all the three approaches are consistent with the causality condition.
Using classical description of spin degrees of freedom, we extend recent formulation of the perfect-fluid hydrodynamics for spin-polarized fluids to the case including dissipation. Our work is based on the analysis of classical kinetic equations for massive particles with spin-1/2, with the collision terms treated in the relaxation time approximation. The kinetic-theory framework determines the structure of viscous and diffusive terms and allows to explicitly calculate a complete set of new kinetic coefficients that characterize dissipative spin dynamics.
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