A lightning strike splits the sky in a fraction of a second, leaving a branched trail. At the same moment, in a tiny superconducting crystal cooled to near absolute zero, an avalanche of magnetic field rushes through — thin fingers of magnetization piercing the material. It seems there is nothing in common between a discharge kilometers long and an event a thousandth of a millimeter across.
New work shows the similarity goes deeper than the outer picture. Both phenomena are governed by the same three-dimensional equation from nonequilibrium physics (the reaction-diffusion-advection equation). Like two orchestras playing from the same score, lightning and quantum avalanches follow identical rules. Their branching, burst sizes, and other characteristics are described by the same numbers — critical exponents. For example, the size distribution of avalanches follows a power law with an exponent of about 1.41, and the fractal dimension of channels is close to 2.5.
The most unexpected thing is the connection between the quantum and classical worlds. The researchers found that the quantum phase coherence of the superconductor, usually hidden from view, manifests in the bends and twists of lightning channels. In other words, the geometry of a lightning discharge carries the imprint of quantum statistics. This opens the way to modeling natural lightning with laboratory superconducting systems and to developing new methods for predicting dangerous discharges from barely noticeable signs.
The exponent 1.41 means that large avalanches are much rarer than small ones, but not as rare as one might expect: this is a universal property of systems in a critical state, from earthquakes to forest fires.
In Stanislaw Lem's novel 'Solaris', the planet-ocean generated mysterious structures governed by unknown laws — now we know that even earthly lightning and quantum vortices may be manifestations of a single code of nature.