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2015

Collisions in Chiral Kinetic Theory

Chen, Jing-Yuan, Son, Dam T., Stephanov, Mikhail A.

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Using a covariant formalism, we construct a chiral kinetic theory Lorentz invariant to order $\mathcal O(\hbar)$ which includes collisions.

We find a new contribution to the particle number current due to the side jumps required by the conservation of angular momentum during collisions.
We also find a conserved symmetric stress-energy tensor as well as the $H$-function obeying Boltzmann's $H$-theorem.
We demonstrate their use by finding a general equilibrium solution and the values of the anomalous transport coefficients characterizing chiral vortical effect.

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Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosić, A. V. Fedorov, R. D. Zhong, J. A. Schneeloch, G. D. Gu, and T. Valla, (2014), arXiv:1412.6543 [cond-mat.str-el]
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M. Neupane et al. , Nature Commun. 5

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Although this is, by far, the most natural form for the collision probability, satisfying nontrivial conditions, we must still consider this form of the collision integral as an educated guess or a conjecture. The correct form of the collision term would be found by deriving the kinetic theory from underlying field theory, which is beyond present scope. Here we only establish that such a consistent theory can be written down in principle

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