Is the shear induced spin polarization non-dissipative?

TL;DR

This paper investigates whether shear-induced spin polarization is non-dissipative by analyzing entropy production, time-reversal symmetry, and linear response, revealing that it may possess dissipative characteristics contrary to some expectations.

Contribution

The study applies quantum kinetic theory and Zubarev's approach to analyze shear-induced polarization, highlighting limitations of current methods in determining its dissipative nature.

Findings

Shear-induced polarization does not directly contribute to entropy production.

Time-reversal symmetry analysis suggests polarization should vanish in coordinate space.

The effects may have a dissipative nature according to Zubarev's approach.

Abstract

The shear-induced polarization plays a crucial role in understanding the local polarization of $\Lambda$ and $\overline{\Lambda}$ hyperons. A key puzzle is whether the shear-induced polarization is non-dissipative or not. In this work, we analyzed the shear-induced polarization and the anomalous Hall effects using the entropy flow and H-theorem introduced from quantum (chiral) kinetic theory. While the shear-induced polarization and the anomalous Hall effect do not directly contribute to the entropy production rate, the perturbations associated with the shear tensor lead to an increase in entropy, similar to the role of the shear tensor in classical kinetic theory. We also examined these effects within the framework of linear response theory using Zubarev's approach. The analysis of time-reversal transformation on the spin current in coordinate space suggests that shear-induced polarization violates time-reversal symmetry and, therefore, should vanish. However, a similar analysis of the Wigner function in phase space does not impose any additional constraints on shear-induced polarization, allowing it to persist in phase space as expected. This discussion indicates that time-reversal analysis in coordinate space alone may not be sufficient to determine whether an effect is dissipative. Furthermore, our analysis based on Zubarev's approach suggests that these effects may indeed possess a dissipative nature. These findings highlight the limitations of the current theoretical framework in fully characterizing the dissipative properties of these phenomena.