Efficient simulation of ultrafast magnetic resonance experiments.

Magnetic resonance spectroscopy and imaging experiments in which spatial dynamics (diffusion and flow) closely coexists with chemical and quantum dynamics (spin-spin couplings, exchange, cross-relaxation, etc.) have historically been very hard to simulate - Bloch-Torrey equations do not support complicated spin Hamiltonians, and the Liouville-von Neumann formalism does not support explicit spatial dynamics. In this paper, we formulate and implement a more advanced simulation framework based on the Fokker-Planck equation. The proposed methods can simulate, without significant approximations, any spatio-temporal magnetic resonance experiment, even in situations when spatial motion co-exists intimately with quantum spin dynamics, relaxation and chemical kinetics.