Linear mode analysis from spin transport equation

Abstract

In this paper, a detailed analysis on normal modes of the linearized hermite collision operator is presented, which comes from linearizing the nonlocal collision term for massive fermions proposed in [1] and neglecting the non-diagonal or polarized part of the transition rate. With the assumption of the conservation of total angular momentum, the kinetic theory we adopt is proved to well describe the equilibrium state and give the right 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 the normal modes as a degenerate perturbation problem and calculate the dispersion relations for our concerned eleven zero modes, which corresponds to all collisional invariants. We find that the results of spinless mode appearing in ordinary hydrodynamics are consistent with available conclusions in some textbooks. As for the new spin-related modes without reference, we obtain the frequencies up to second-order in wave vector of which the second corrections are only formal solutions to be further determined. In addition, the relaxation of spin density is related to our linear mode analysis, which shall play a big role in investigating the issues of the local spin polarization in the relativistic heavy-ion collisions.

Relativistic spin-magnetohydrodynamics

“…Given that several gradients are present in all dissipative currents, the present first-order theory may prove to be causal and stable, even though it is formulated in the Landau frame. Therefore it is important to perform a stability analysis [88][89][90] of Eqs. ( 35)- (38).…”

Semi-classical kinetic theory for massive spin-half fermions with leading-order spin effects

“…[27,28]. Other similar approaches used concepts of thermodynamic equilibrium [29], effective action [30][31][32], entropy current [33][34][35][36][37], statistical operator [38], non-local collisions [39][40][41][42][43][44][45][46][47], chiral kinetic theory [39,48], and holographic duality [49][50][51].…”