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Describing how matter behaves at the quantum-mechanical level is notoriously hard, because the equations get so difficult to solve once there is more than a handful of particles involved. But a new experiment shows that the fine details might not matter too much – and that, if we “squint” at a many-particle quantum system to blur them, how the system changes over time can look surprisingly like the familiar classical process of diffusion.

Figuring out the exact trajectories of particles of ink in a glass of water as they are battered this way and that by water molecules is difficult. But you do not need to keep track of every molecule because. Fick’s law of diffusion says that the flow of material is simply proportional to its concentration gradient.

Fick’s law is an example of coarse-graining that is commonly used in hydrodynamics. For example, a fluid can be considered a collection of little “parcels”, each containing countless molecules, which move frictionally past one another.

Researchers have recently sought to describe quantum-mechanical many-particle systems using such an approach. Say you have a material containing a bunch of quantum spins that interact with one another, you create a local “blob” of oriented spins and calculate how it will then spread through the system.

“Hydrodynamics is generally the study of how a system goes from local equilibrium to global equilibrium”, says Joel Moore of the University of California at Berkeley. The equations of fluid mechanics, he says, assume that any detailed information about the initial state – where the particles are and how they are moving – is quickly lost once they have experienced just a few interactions (collisions) with others. “Then the fluid equations describe everything on longer time scales, from microseconds to years, very accurately.”

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