2015/03/24 by Robin A. Damion, Damion, Robin A.
Biochemistry, Genetics and Molecular Biology · Chemistry · Physics and Astronomy · #Advanced NMR Techniques and Applications #FOS: Physical sciences #Molecular spectroscopy and chirality #Protein Structure and Dynamics #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1503.06880
25 pages
arxiv created 2015/03/24 · openalex publication_date 2015/03/24 · arxiv updated 2015/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The concept of a propagator is useful and is a well-known object in diffusion NMR experiments. Here, we investigate the related concept; the propagator for the magnetisation or the Green's function of the Torrey-Bloch equations. The magnetisation propagator is constructed by defining functions such as the Hamiltonian and Lagrangian and using these to define a path integral. It is shown that the equations of motion derived from the Lagrangian produce complex-valued trajectories (classical paths) and it is conjectured that the end-points of these trajectories are real-valued. The complex nature of the trajectories also suggests that the spin degrees of freedom are also encoded into the trajectories and this idea is explored by explicitly modeling the spin or precessing magnetisation by anticommuting Grassmann variables. A pseudoclassical Lagrangian is constructed by combining the diffusive (bosonic) Lagrangian with the Grassmann (fermionic) Lagrangian, and performing the path integral over the Grassmann variables recovers the original Lagrangian that was used in the construction of the propagator for the magnetisation. The trajectories of the pseudoclassical model also provide some insight into the nature of the end-points.