Fermi acceleration in rotating drums

The paper proves (i) no Fermi acceleration without gravity via conservation of the rotating-frame energy EF and an explicit uniform bound EK(t) ≤ 2 EF + 2 M ω^2 R^2, and (ii) with gravity, energy can be made arbitrarily large: for Lambertian reflections in a rotating circle with conserved speed in F at impacts there is a positive probability to reach any prescribed level (Cor. 4.6), and for specular reflections one can deterministically realize unbounded growth with a C∞ boundary contained in an arbitrarily small annulus around the circle (Cor. 4.7). These are all explicitly established in the paper, e.g., EF conservation and the EK bound (Propositions 2.1–2.2) and the rotating-observer equations (Section 5.2) underpin the arguments . The candidate solution’s Part A matches Proposition 2.2 essentially line-for-line, while Parts B–C pursue a different but viable route: a direct per-flight energy increment estimate in F using dEF/dt = −g⟨vF, R(−ωt)ey⟩ (consistent with the rotating-frame equations) and a “good-window” probabilistic amplification for Lambertian reflections, plus a micro-mirror construction for the specular near-disc case. The paper instead uses a two-point pseudo-Lambertian model and continuity/probability arguments to obtain positive-probability growth (Cor. 4.6) and a boundary perturbation to realize a deterministic growth trajectory (Cor. 4.7) . Overall, the model’s solution aligns with the paper’s claims, differing mainly in proof technique for Part B.