The theory of spin transport in quantum systems, as compared to charge transport, is still in a preliminary stage. Whenever the spin operator does not commute with the unperturbed Hamiltonian operator, as it happens in the so-called Rashba insulators, the lack of commutativity poses technical and conceptual problems for the theory.

In my talk, I will first address some foundational questions in spin transport theory. Then, I will present a new formula for the transverse spin conductivity in gapped (periodic) quantum systems, which generalizes to spin the celebrated double-commutator formula for charge conductivity, sometimes dubbed Kubo-Chern formula. As a corollary, one obtains that whenever the spin is (almost) conserved, the transverse spin conductivity is (approximately) equal to the spin-Chern number.

The method of proof relies on the characterization of a non-equilibrium almost-stationary state (NEASS), which well approximates the physical state of the system (in the sense of space-adiabatic perturbation theory) and allows moreover to compute the response of the adiabatic spin current as the trace per unit volume of the spin current operator times the NEASS.

The talk is based on results obtained jointly with G. Marcelli and S. Teufel, and with G. Marcelli and C. Tauber.

To get an invitation to the zoom-meeting, please contact one of the organisers.