The linear mode analysis and spin relaxation

Abstract

In this paper, a detailed analysis on normal modes of the linearized Hermite collision operator is presented, which follows from linearizing spin Boltzmann equation for massive fermions proposed in \cite{Weickgenannt:2021cuo} with the non-diagonal part of the transition rate neglected and approximating what we got with a mutilated operator. With the assumption of total angular momentum conservation, the collision term is proved to well describe the equilibrium state and gives proper interpretation for collisional invariants, thus is relevant for the research on local spin polarization. Following the familiar fashion as used in quantum mechanics, we treat the problem of solving normal modes as a degenerate perturbation problem and calculate the dispersion relations for intriguing eleven zero modes, which form one-to-one correspondence to all collisional invariants. We find that the results of spinless modes appearing in ordinary hydrodynamics are consistent with available conclusions in textbooks. As for spin-related modes, we obtain the frequencies up to second order in wave vector and relate them with the dissipation of spin density fluctuation. In addition, the ratio of two relaxation time scales for spin and momentum is shown as a function of reduced mass, which reads that based on present framework spin equilibration is almost as slow as momentum equilibration as far as the strange quark spins in quark gluon plasma (QGP) are concerned.

References in corpus (4)

• Collective longitudinal polarization in relativistic heavy-ion collisions at very high energy
• Fate of spin polarization in a relativistic fluid: An entropy-current analysis
• Global $\Lambda$ Polarization in high energy collisions
• Lambda hyperon polarization in relativistic heavy ion collisions from the chiral kinetic approach

Cited by in corpus (13)

• Stability studies of first order spin-hydrodynamic frameworks
• Damping of spin waves
• Boost invariant spin hydrodynamics within the first order in derivative expansion
• Linear mode analysis from spin transport equation
• Resummed spin hydrodynamics from quantum kinetic theory
• Cross effects in spin hydrodynamics: A revisit Entropy analysis and statistical operator
• An introduction to relativistic spin hydrodynamics
• Collective dynamics of polarized spin-half fermions in relativistic heavy-ion collisions
• Propagation of spin channel waves
• Relaxation time approximation revisited and non-analytical structure in retarded correlators
• Anisotropic linear waves and breakdown of the momentum expansion in spin magnetohydrodynamics
• Normal mode analysis within a mutilated relaxation time approximation
• Normal mode analysis within relativistic massive transport