Derivation of a linear collision operator for the spinorial Wigner equation and its semiclassical limit

TL;DR

This paper derives a linear collision operator for the spinorial Wigner equation, connecting quantum dynamics with semiclassical spin transport models like Bloch and Boltzmann equations, relevant for spintronics.

Contribution

It provides a systematic derivation of a quantum collision operator and its semiclassical limit, enabling improved modeling of spin-polarized transport.

Findings

Derivation of a matrix-form collision operator for spin decoherence.

Connection of quantum dynamics to semiclassical spin-transport models.

Systematic inclusion of quantum corrections in spin transport equations.

Abstract

We systematically derive a linear quantum collision operator for the spinorial Wigner transport equation from the dynamics of a composite quantum system. For suitable two particle interaction potentials, the particular matrix form of the collision operator describes spin decoherence or even spin depolarization as well as relaxation towards a certain momentum distribution in the long time limit. It is demonstrated that in the semiclassical limit the spinorial Wigner equation gives rise to several semiclassical spin-transport models. As an example, we derive the Bloch equations as well as the spinorial Boltzmann equation, which in turn gives rise to spin drift-diffusion models which are increasingly used to describe spin-polarized transport in spintronic devices. The presented derivation allows to systematically incorporate Born-Markov as well as quantum corrections into these models.