Universal spatial correlations in random spinor fields

Abstract

We identify universal spatial fluctuations in systems with non trivial spin
dynamics. To this end we calculate by exact numerical diagonalization a variety
of experimentally relevant correlations between spinor amplitudes, spin
polarizations and spin currents both in the bulk and near the boundary of a
confined two-dimensional clean electron gas in the presence of spin-orbit
interaction and a single magnetic impurity. We support or claim of universality
with the excellent agreement between the numerical results and
system-independent spatial correlations of a random field defined on both the
spatial and spin degrees of freedom. A rigorous identity relating our universal
predictions with response functions provides a direct physical interpretation
of our results in the framework of linear response theory.