Undecidability and Quantum Mechanics
Recently, great attention has been devoted to the problem of the undecidability of specific questions in quantum mechanics. In this context, it has been shown that the problem of the existence of a spectral gap, i.e., energy difference between the ground state and the first excited state, is algorit...
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| Format: | Article |
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MDPI AG
2022-08-01
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| Series: | Encyclopedia |
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| Online Access: | https://www.mdpi.com/2673-8392/2/3/103 |
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| author | Canio Noce Alfonso Romano |
| author_facet | Canio Noce Alfonso Romano |
| author_sort | Canio Noce |
| collection | DOAJ |
| description | Recently, great attention has been devoted to the problem of the undecidability of specific questions in quantum mechanics. In this context, it has been shown that the problem of the existence of a spectral gap, i.e., energy difference between the ground state and the first excited state, is algorithmically undecidable. Using this result herein proves that the existence of a quantum phase transition, as inferred from specific microscopic approaches, is an undecidable problem, too. Indeed, some methods, usually adopted to study quantum phase transitions, rely on the existence of a spectral gap. Since there exists no algorithm to determine whether an arbitrary quantum model is gapped or gapless, and there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics, it infers that the existence of quantum phase transitions is an undecidable problem. |
| first_indexed | 2024-03-10T00:11:04Z |
| format | Article |
| id | doaj.art-58352985b30f42b2baf694088ccb8508 |
| institution | Directory Open Access Journal |
| issn | 2673-8392 |
| language | English |
| last_indexed | 2024-03-10T00:11:04Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Encyclopedia |
| spelling | doaj.art-58352985b30f42b2baf694088ccb85082023-11-23T16:00:12ZengMDPI AGEncyclopedia2673-83922022-08-01231517152710.3390/encyclopedia2030103Undecidability and Quantum MechanicsCanio Noce0Alfonso Romano1Dipartimento di Fisica “E. R. Caianiello”, Università degli Studi di Salerno, I-84084 Fisciano, ItalyDipartimento di Fisica “E. R. Caianiello”, Università degli Studi di Salerno, I-84084 Fisciano, ItalyRecently, great attention has been devoted to the problem of the undecidability of specific questions in quantum mechanics. In this context, it has been shown that the problem of the existence of a spectral gap, i.e., energy difference between the ground state and the first excited state, is algorithmically undecidable. Using this result herein proves that the existence of a quantum phase transition, as inferred from specific microscopic approaches, is an undecidable problem, too. Indeed, some methods, usually adopted to study quantum phase transitions, rely on the existence of a spectral gap. Since there exists no algorithm to determine whether an arbitrary quantum model is gapped or gapless, and there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics, it infers that the existence of quantum phase transitions is an undecidable problem.https://www.mdpi.com/2673-8392/2/3/103undecidabilityspectral gapquantum phase transition |
| spellingShingle | Canio Noce Alfonso Romano Undecidability and Quantum Mechanics Encyclopedia undecidability spectral gap quantum phase transition |
| title | Undecidability and Quantum Mechanics |
| title_full | Undecidability and Quantum Mechanics |
| title_fullStr | Undecidability and Quantum Mechanics |
| title_full_unstemmed | Undecidability and Quantum Mechanics |
| title_short | Undecidability and Quantum Mechanics |
| title_sort | undecidability and quantum mechanics |
| topic | undecidability spectral gap quantum phase transition |
| url | https://www.mdpi.com/2673-8392/2/3/103 |
| work_keys_str_mv | AT canionoce undecidabilityandquantummechanics AT alfonsoromano undecidabilityandquantummechanics |