{"title":"从基质/膜对应关系看模糊球的大小和形状","authors":"Hai H. Vo, Nguyen H. Nguyen, Trung V. Phan","doi":"arxiv-2409.11435","DOIUrl":null,"url":null,"abstract":"We study the size and shape statistics of ground state fuzzy spheres when\nprojected onto the transverse plane, utilizing the regularized SU(N=2) matrix\nmodel in D=(1+3)-dimensional spacetime. We show that they appear as ellipses,\nfrom matrix/membrane correspondence. With our numerical and analytical\napproximation for the ground state wavefunction, we provide estimations for\ntheir expected surface areas, perimeters, eccentricities, and shape-parameters.\nThese geometric constants of quantum membranes deviate drastically from\nclassical mechanics.","PeriodicalId":501226,"journal":{"name":"arXiv - PHYS - Quantum Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Size and Shape of Fuzzy Spheres from Matrix/Membrane Correspondence\",\"authors\":\"Hai H. Vo, Nguyen H. Nguyen, Trung V. Phan\",\"doi\":\"arxiv-2409.11435\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the size and shape statistics of ground state fuzzy spheres when\\nprojected onto the transverse plane, utilizing the regularized SU(N=2) matrix\\nmodel in D=(1+3)-dimensional spacetime. We show that they appear as ellipses,\\nfrom matrix/membrane correspondence. With our numerical and analytical\\napproximation for the ground state wavefunction, we provide estimations for\\ntheir expected surface areas, perimeters, eccentricities, and shape-parameters.\\nThese geometric constants of quantum membranes deviate drastically from\\nclassical mechanics.\",\"PeriodicalId\":501226,\"journal\":{\"name\":\"arXiv - PHYS - Quantum Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - Quantum Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11435\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11435","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Size and Shape of Fuzzy Spheres from Matrix/Membrane Correspondence
We study the size and shape statistics of ground state fuzzy spheres when
projected onto the transverse plane, utilizing the regularized SU(N=2) matrix
model in D=(1+3)-dimensional spacetime. We show that they appear as ellipses,
from matrix/membrane correspondence. With our numerical and analytical
approximation for the ground state wavefunction, we provide estimations for
their expected surface areas, perimeters, eccentricities, and shape-parameters.
These geometric constants of quantum membranes deviate drastically from
classical mechanics.
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