• Open Access

Linear mode analysis and spin relaxation

Jin Hu
Phys. Rev. D 105, 096021 – Published 18 May 2022

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 [Phys. Rev. D 104, 016022 (2021)] with the nondiagonal 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 proven 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 a wave vector and relate them with the dissipation of spin density fluctuation. In addition, the ratio of two relaxation timescales 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.

  • Figure
  • Received 9 March 2022
  • Accepted 8 May 2022

DOI:https://doi.org/10.1103/PhysRevD.105.096021

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nuclear PhysicsFluid Dynamics

Authors & Affiliations

Jin Hu*

  • Department of Physics, Tsinghua University, Beijing 100084, China

  • *hu-j17@mails.tsinghua.edu.cn

Article Text

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Issue

Vol. 105, Iss. 9 — 1 May 2022

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