{"title":"Hear π from Quantum Galperin Billiards","authors":"Y. Cai, Fu-Lin Zhang","doi":"10.1139/cjp-2022-0262","DOIUrl":null,"url":null,"abstract":"Galperin [Regul. Chaotic. Dyn. 8, 375 (2003)] introduced an interesting method to learn the digits of π by counting the collisions of two billiard balls and a hard wall. This paper studies two quantum versions of the Galperin billiards. It is shown that the digits of π can be observed in the phase shifts of the quantum models.","PeriodicalId":9413,"journal":{"name":"Canadian Journal of Physics","volume":"18 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1139/cjp-2022-0262","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
Galperin [Regul. Chaotic. Dyn. 8, 375 (2003)] introduced an interesting method to learn the digits of π by counting the collisions of two billiard balls and a hard wall. This paper studies two quantum versions of the Galperin billiards. It is shown that the digits of π can be observed in the phase shifts of the quantum models.
期刊介绍：
The Canadian Journal of Physics publishes research articles, rapid communications, and review articles that report significant advances in research in physics, including atomic and molecular physics; condensed matter; elementary particles and fields; nuclear physics; gases, fluid dynamics, and plasmas; electromagnetism and optics; mathematical physics; interdisciplinary, classical, and applied physics; relativity and cosmology; physics education research; statistical mechanics and thermodynamics; quantum physics and quantum computing; gravitation and string theory; biophysics; aeronomy and space physics; and astrophysics.
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