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In 1953 Albert Overhauser suggested a method to enhance the alignment of nuclear spins for metals placed in magnetic fields by irradiating the electron spins. This formed the start of the Dynamic Nuclear Polarization technique for hyperpolarizing nuclei during NMR experiments. The current “Renaissance” of this technique has convinced us to try to understand the underlying process of polarization transfer from the electrons to the nuclei in amorphous organic solid solutions containing radicals.

Many natural and industrial settings involve dilute systems of reacting particles transported by an unsteady fluid flow. We consider the simple case of an annihilation process A + A → Ø with a given rate when two particles are within a finite radius of interaction. The system is described in terms of the joint n-point number spatial density that it is shown to obey a hierarchy of transport equations. An analytic solution is obtained in either the dilute or the long-time limit by using a Lagrangian approach where statistical averages are performed along non-reacting trajectories. In this limit, we show that the moments of the number of particles have an exponential decay rather than the algebraic prediction of standard mean-field approaches. The effective reaction rate is then related to Lagrangian pair statistics by a large-deviation principle. A phenomenological model is introduced to study the qualitative behavior of the effective rate as a function of the interaction length, the degree of chaoticity of the dynamics and the compressibility of the carrier flow. Exact computations, obtained via a Feynman-Kac approach, in a smooth, compressible, random delta-correlated-in-time Gaussian velocity field support the proposed heuristic approach.
(joint work with M. Cencini and G. Krstulovic)