Eternal Acceleration: Quantum Ball vs. Classical ⚡ экспресс
Original: "On the original Ulam's problem and its quantization"
The classical and quantum versions of a 'bouncy' model behave in opposite ways.
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A classical ball squeezed between two walls behaves like a diligent student: it bounces around and returns to its place. The quantum one, however, breaks free — its energy grows without limit. This difference can shed light on how nature creates cosmic ray particles.
🎯 If you rhythmically hit a ball with a racket, it bounces higher and higher — a everyday manifestation of Fermi acceleration.
E \propto t^2
In the quantum case, energy E ~ t², i.e., grows as the square of time.