Enrico Fermi described a particle as a swing between two walls that alternately come together and move apart. This is how he explained how particles in supernova explosions are accelerated to nearly the speed of light.

It turned out that in our familiar world, such a 'swing' accelerator quickly fades: the particle loses momentum and returns. But in the microworld, governed by quantum laws, things are different: the longer the kicks go on, the stronger the acceleration — the energy grows quadratically with time.

Scientists also figured out how to catch extremely rare scenarios from ordinary physics where the particle does fly off to infinity. It turned out that in the quantum version, the set of allowed energies plays a key role — essentially, an internal 'schedule' of kicks. These findings will help understand real accelerators, for example, around neutron stars.