Equilibrium Spin Distribution From Detailed Balance

Abstract

As the core ingredient for spin polarization, the equilibrium spin distribution function that eliminates the collision terms is derived from the detailed balance principle. The kinetic theory for interacting fermionic systems is applied to the Nambu–Jona-Lasinio model at quark level. Under the semi-classical expansion with respect to $$\hbar $$ ħ , the kinetic equations for the vector and axial-vector distribution functions are obtained with collision terms. For an initially unpolarized system, spin polarization can be generated at the first order of $$\hbar $$ ħ from the coupling between the vector and axial-vector charges. Different from the classical transport theory, the collision terms in a quantum theory vanish only in global equilibrium with Killing condition.

Exact equilibrium distributions in statistical quantum field theory with rotation and acceleration: Dirac field

“…In this paper, we extend that method to a free quantum field of any spin and particularly the free Dirac field of JHEP10(2021)077 spin 1/2 particles. We obtain exact expressions of several physical quantities, including the covariant Wigner function, which is of great relevance for the relativistic kinetic theory of massive fermions [2][3][4][5][6][7][8] as well as the spin density matrix and the spin polarization vector, which are of special interest for the phenomenology of relativistic heavy ion collisions [9]. We demonstrate the viability of our method by comparing the newly found results with those known in the literature for the two special cases of equilibrium with pure acceleration and pure rotation and with those known at the leading perturbative order in thermal vorticity.…”

Foundations and Applications of Quantum Kinetic Theory

“…Furthermore, even though the global-equilibrium solution of the Wigner functions for massive fermions can be acquired by the detailed balance of the QKT as shown in Refs. [334,395], the local-equilibrium solution in connection with the result obtained in the CKT [168] remains to be solved.…”

“…It is dubbed as the spin-polarization term and responsible for the polarization of particles via the intertwined dynamics of vector-charge transport due to spin-orbit interaction. Albeit not in QCD, a concrete example can be found in the application of AKE to the Nambu-Jona-Lasinio model [395,340], where the equilibrium value of A µ as in Eq. (9.45) triggered by nonzero vorticity is acquired via the detailed balance with a vanishing collision term.…”

Linear mode analysis from spin transport equation

“…Therefore it is necessary to derive the quantum transport equations with proper collision terms, which must incorporate spin as the independent variable and account for the coupling between spin and orbit. To note, the related developments in spin transport can be found in [1,[26][27][28][29]. Accounting for the complexity and non-linearity, these transport equations are hard to solve.…”