Shear induced polarization: Collisional contributions

It has been realized that thermal shear plays a similar role as thermal vorticity in polarizing spin of particles in heavy ion collisions. We point out that shear has a fundamental difference that it leads to particle redistribution in the medium. The redistribution gives rise to an additional contribution to spin polarization through the self-energy, which is parametrically the same order as the one considered so far in the literature. The self-energy contribution is in general gauge dependent. We introduce double gauge links stretching along the Schwinger-Keldysh contour to restore gauge invariance. We also generalize the straight path to adapt to the Schwinger-Keldysh contour. We find another contribution associated with the gauge link, which is also parametrically the same order. We illustrate the two contributions with a massive probe fermion in massless QED plasma with shear. A modest suppression of spin polarization is found from the combined contributions when the probe fermion has momentum much greater than the temperature.Comment: 29 pages, 5 figure

C.E.O. academic experience and firm sustainable growth

Chief executive officers (C.E.O.s) play a dominant role in firm decision- makings and operations, and their characteristics will affect firm sustainable growth. This study investigates whether C.E.O. academic experience affects firm sustainable growth. Using a sample from China, we find that C.E.O. academic experience is positively related to firm sustainable growth, and the effect is pronounced for high-tech firms. Further analyses demonstrate that the results are robust to alternative measures and controlling for endogeneity problems. Finally, the channel analysis shows that the effect is partially driven by firm innovation and internal control

Local Equilibrium Spin Distribution From Detailed Balance

As the core ingredient for spin polarization, the local equilibrium spin distribution function 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 $\hbar$ and non-perturbative expansion with respect to $N_c$, the kinetic equations for the vector and axial-vector distribution functions are derived with collision terms. It is found that, for an initially unpolarized system, non-zero spin polarization can be generated at the order of $\hbar$ from the coupling between the vector and axial-vector charges. The local equilibrium spin polarization is derived from the requirement of detailed balance. It arises from the thermal vorticity and is orthogonal to the particle momentum.Comment: 13 page