title: Fokker-Planck formalism in magnetic resonance simulations.
abstract: This paper presents an overview of the Fokker-Planck formalism for non-biological magnetic resonance simulations, describes its existing applications and proposes some novel ones. The most attractive feature of Fokker-Planck theory compared to the commonly used Liouville - von Neumann equation is that, for all relevant types of spatial dynamics (spinning, diffusion, stationary flow, etc.), the corresponding Fokker-Planck Hamiltonian is time-independent. Many difficult NMR, EPR and MRI simulation problems (multiple rotation NMR, ultrafast NMR, gradient-based zero-quantum filters, diffusion and flow NMR, off-resonance soft microwave pulses in EPR, spin-spin coupling effects in MRI, etc.) are simplified significantly in Fokker-Planck space. The paper also summarises the author's experiences with writing and using the corresponding modules of the Spinach library - the methods described below have enabled a large variety of simulations previously considered too complicated for routine practical use.
authors.affiliation: School of Chemistry, University of Southampton, University Road, Southampton SO17 1BJ, UK. Electronic address: i.kuprov@soton.ac.uk.
authors.forename: Ilya
authors.initials: I
authors.lastname: Kuprov
keywords: Magnetic resonance; Simulation; Spin dynamics