Title: An exactly solvable model for Dynamic Nuclear polarization,
Abstract: We introduce a solvable model of driven fermions that elucidates the role of
the localization transition in driven disordered magnets, as used in the
context of dynamic nuclear polarization. Instead of spins, we study a set of
non-interacting fermions that are coupled locally to nuclear spins and tend to
hyperpolarize them. The induced hyperpolarization is a fingerprint of the
driven steady state of the fermions, which undergo an Anderson Localization
(AL) transition upon increasing the disorder. Our central result is that the
maximal hyperpolarization level is always found close to the localization
transition. In the limit of small nuclear moments the maximum is pinned to the
transition, and the hyperpolarization is strongly enhanced by multi-fractal
correlations in the critical state of the nearly localized driven system, its
magnitude reflecting multi-fractal scaling.