Particles in one spatial dimension behave completely differently than those in one plane. But what happens when the number of dimensions lies in between? Physicists have for the first time studied the wavefunctions of electrons locked in fractal geometries.
The number of spatial dimensions is decisive for many processes in nature. A mouse in a narrow drain pipe, for example, could hardly escape an oncoming cat, while it would have a much easier time in an open field. Birds, which also use the third dimension of space, find it easiest to escape from a hungry hunter.
It's the same in physics. The behavior of electrons depends greatly on whether they are in one, two, or three-dimensional materials. In two and three dimensions, the negatively charged particles can simply avoid each other, their movement is reminiscent of that of a liquid. But in only one dimension electrons have it harder. Because they cannot avoid each other over long distances, the repulsive electromagnetic forces affect them much more than in higher dimensions. This has extraordinary consequences: if the particles are set in motion, for example, their spin suddenly oscillates independently of themselves. It seems as if there were "spin waves" and "charge waves" that propagate independently of each other.
Researchers have extensively studied the extent to which physical phenomena depend on the dimension of a system. They have restricted themselves to integer dimensions. Now, for the first time, physicists around Sander Kempkes from the University of Utrecht have researched the wave functions of electrons in crystals whose dimension is between one and two…