On the original Ulam's problem and its quantization
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911065749585920 |
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| author | Dong, Changguang Zhou, Jing |
| author_facet | Dong, Changguang Zhou, Jing |
| contents | In this paper we show that under general resonance the classical piecewise linear Fermi-Ulam accelerator behaves substantially different from its quantization in the sense that the classical accelerator exhibits typical recurrence and non-escaping while the quantum version enjoys quadratic energy growth in general. We also describe a procedure to locate the escaping orbits, though exceptionally rare in the infinite-volume phase space, for the classical accelerators, which in particular include Ulam's very original proposal and the linearly escaping orbits therein in the existing literature, and hence provide a complete (modulo a null set) answer to Ulam's original question. For the quantum accelerators, we reveal under resonance the direct and explicit connection between the energy growth and the shape of the quasi-energy spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_01684 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the original Ulam's problem and its quantization Dong, Changguang Zhou, Jing Dynamical Systems Mathematical Physics Quantum Physics 37N05, 81Q50 (Primary), 35Q41, 37E10 (Secondary) In this paper we show that under general resonance the classical piecewise linear Fermi-Ulam accelerator behaves substantially different from its quantization in the sense that the classical accelerator exhibits typical recurrence and non-escaping while the quantum version enjoys quadratic energy growth in general. We also describe a procedure to locate the escaping orbits, though exceptionally rare in the infinite-volume phase space, for the classical accelerators, which in particular include Ulam's very original proposal and the linearly escaping orbits therein in the existing literature, and hence provide a complete (modulo a null set) answer to Ulam's original question. For the quantum accelerators, we reveal under resonance the direct and explicit connection between the energy growth and the shape of the quasi-energy spectra. |
| title | On the original Ulam's problem and its quantization |
| topic | Dynamical Systems Mathematical Physics Quantum Physics 37N05, 81Q50 (Primary), 35Q41, 37E10 (Secondary) |
| url | https://arxiv.org/abs/2506.01684 |