  Dynamic nuclear polarization (DNP) is an out-of-equilibrium method for
generating non-thermal spin polarization which provides large signal
enhancements in modern diagnostic methods based on nuclear magnetic resonance.
A particular instance is cross effect DNP, which involves the interaction of
two coupled electrons with the nuclear spin ensemble. Here we develop a theory
for this important DNP mechanism and show that the non-equilibrium nuclear
polarization build-up is effectively driven by three-body incoherent Markovian
dissipative processes involving simultaneous state changes of two electrons and
one nucleus. Our theoretical approach allows for the first time simulations of
the polarization dynamics on an individual spin level for ensembles consisting
of hundreds of nuclear spins. The insight obtained by these simulations can be
used to find optimal experimental conditions for cross effect DNP and to design
tailored radical systems that provide optimal DNP efficiency.
