A handful of coins drops onto a table — heads and tails land wherever they please. The same goes for an instantaneous snapshot of a quantum chain: in some places a particle is present, in others it is not. But behind the disorder lurks a precise angle.
In this work, a chain of particles closed into a ring was considered. It was divided into four arcs: two were measured, two were left untouched. From the occupied and empty sites in the measured arcs, the angle δL was computed. It turned out that this angle does not depend on what lies in the unmeasured arcs. It is determined solely by the snapshot itself.
As the ring grows, the angle begins to blur according to a known mathematical rule, just as heat spreads around a circle. This means that quantum snapshots, usually considered pure chaos, carry geometry. Randomness turns out to be not entirely random.
The angle from a random snapshot behaves like heat: as the system grows, it spreads around the circle just as heat diffuses along a ring.