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The linear mode analysis and spin relaxation
High Energy Physics - Phenomenology · Submitted 27 Apr 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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.
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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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.78 | 0.86 | 0.07 | asserted 0.99 |
| s1 | 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. | interpretation 0.68 | 0.82 | 0.18 | asserted 1.00 |
| s2 | 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. | method 0.90 | 0.95 | 0.14 | asserted 1.00 |
| s3 | We find that the results of spinless modes appearing in ordinary hydrodynamics are consistent with available conclusions in textbooks. | result 0.95 | 0.77 | 0.06 | asserted 0.64 |
| s4 | 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. | result 0.99 | 0.96 | 0.16 | asserted 1.00 |
| s5 | 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. | result 0.78 | 0.91 | 0.47 | asserted 0.91 |
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Original 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.
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6 arXiv papers cite this in 9 sentences
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Furthermore, compared to the results of Ref. [ref] , which also considered nonlocal collisions, the separation of our relaxation time scales is larger.
Damping of spin waves · Conclusion · 0.93
Cites it as background 4 papers
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Recently, several works have taken on the task of computing the spin-relaxation timescale [ref] , with results depending on the microscopic theory employed.
Damping of spin waves · Introduction · 0.92
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Such theoretical intricacies associated with the mode analysis has also been studied for the relativistic magnetohydrodynamics [ref] , spin hydrodynamics [ref] , chiral hydrodynamics [ref] , etc.
Stability studies of first order spin-hydrodynamic frameworks · Introduction · 0.92
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These developments eventually led to the studies of spin modes and associated spin relaxation timescales [ref] .
Relativistic spin hydrodynamics with momentum and spin-dependent relaxation time · Introduction · 0.95
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