Duality of the spin and density dynamics for two-dimensional electrons with a spin-orbit coupling

We study spin dynamics in a two-dimensional electron gas with a pure gauge non-Abelian spin-orbit field, for which systems with balanced Rashba and Dresselhaus spin-orbit couplings, and the (110)-axis grown GaAs quantum wells are typical examples. We demonstrate the duality of the spin evolution and the electron-density dynamics in a system without spin-orbit coupling, which considerably simplifies and deepens the analysis of spin-dependent processes. This duality opens a venue for the understanding of this class of systems, highly interesting for their applications in spintronics, through known properties of the systems without spin-orbit coupling.