Diffusion exchange spectroscopy (DEXSY) measures molecular exchange between compartments — water crossing a cell membrane, molecules moving between pore spaces, substrates transferring between phases. The technique applies two sequential diffusion-encoding gradients separated by a mixing time. If molecules exchange compartments during the mixing period, the signal reveals cross-peaks at positions corresponding to the two compartments. The appearance of off-diagonal signal is interpreted as evidence that molecules moved from one compartment to another. The technique has been applied to biological tissue, porous media, and emulsions to quantify exchange rates.
Cai, Williamson, and Basser (arXiv:2603.27907, March 2026) demonstrate that a single compartment with reflecting boundaries and no exchange at all can produce identical exchange signals. The mechanism is purely geometric: diffusive mixing of spin coherences initially near versus far from the boundary creates apparent cross-peaks. Spins near the walls experience restricted diffusion differently from spins near the center, and as the mixing time increases, the spatial distribution of magnetization relaxes through modes of the Laplacian operator. The apparent exchange rate k equals π²D/L², where D is diffusivity and L is compartment size — precisely the first non-zero eigenvalue of the diffusion operator.
This is not an edge case. The geometric artifact produces exchange-like signals at experimentally realistic mixing times, in exactly the parameter regime where real exchange measurements are typically performed. A researcher measuring exchange between two compartments cannot distinguish, from the DEXSY signal alone, between genuine molecular transport across a barrier and spatial redistribution of coherences within a single compartment.
The structural observation: the measurement was designed to detect a process (barrier permeation) but is equally sensitive to a geometric effect (modal relaxation) that mimics the process without involving it. The off-diagonal signal does not mean “molecules crossed a boundary.” It means “the signal structure changed during the mixing time,” and boundary crossing is only one of the mechanisms that produces such changes. The interpretation was more specific than the measurement.