Eternal Acceleration: Quantum Ball vs. Classical ⚡ экспресс
It is shown that under general resonance, the classical piecewise-linear Fermi–Ulam accelerator fundamentally differs from its quantum counterpart: the classical system is dominated by returns and lack of escape, whereas the quantum version exhibits quadratic energy growth. A procedure for detecting escaping orbits of the classical accelerator is described; despite their exceptional rarity in the infinite phase space, trajectories have been found, including Ulam's original proposal and linearly escaping orbits, which fully (up to a set of measure zero) resolve his question. For the quantum accelerator at resonance, a direct explicit link is revealed between the rate of energy growth and the shape of the quasienergy spectrum.
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.
🎯 If you rhythmically hit a ball with a racket, it bounces higher and higher — a everyday manifestation of Fermi acceleration.