Quantum knots and the number of knot mosaics
DC Field | Value | Language |
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dc.contributor.author | Oh, Seungsang | - |
dc.contributor.author | Hong, Kyungpyo | - |
dc.contributor.author | Lee, Ho | - |
dc.contributor.author | Lee, Hwa Jeong | - |
dc.date.accessioned | 2021-09-04T18:39:37Z | - |
dc.date.available | 2021-09-04T18:39:37Z | - |
dc.date.created | 2021-06-15 | - |
dc.date.issued | 2015-03 | - |
dc.identifier.issn | 1570-0755 | - |
dc.identifier.uri | https://scholar.korea.ac.kr/handle/2021.sw.korea/94258 | - |
dc.description.abstract | Lomonaco and Kauffman developed a knot mosaic system to introduce a precise and workable definition of a quantum knot system. This definition is intended to represent an actual physical quantum system. A knot (m, n)-mosaic is an m x n matrix of mosaic tiles (T-0 through T-10 depicted in the introduction) representing a knot or a link by adjoining properly that is called suitably connected. D(m, n) is the total number of all knot (m, n)-mosaics. This value indicates the dimension of the Hilbert space of these quantum knot system. D-(m,D- n) is already found for m, n <= 6 by the authors. In this paper, we construct an algorithm producing the precise value of D-(m,D- n) for m, n >= 2 that uses recurrence relations of state matrices that turn out to be remarkably efficient to count knot mosaics. D(m,n) = 2 parallel to (Xm-2 + Om-2)(n-2) parallel to where 2(m-2) x 2(m-2) matrices Xm-2 and Om-2 are defined by Xk+1 = [X-k O-k] [O-k X-k] and Ok+1 = [O-k X-k] [X-k 4 O-k] for k = 0, 1, .... , m - 3, with 1 x 1 matrices X-0 = [1] and O-0 = [1]. Here parallel to N parallel to denotes the sum of all entries of a matrix N. For n = 2, (Xm-2 + Om-2)(0) means the identity matrix of size 2(m-2) x 2(m-2). | - |
dc.language | English | - |
dc.language.iso | en | - |
dc.publisher | SPRINGER | - |
dc.title | Quantum knots and the number of knot mosaics | - |
dc.type | Article | - |
dc.contributor.affiliatedAuthor | Oh, Seungsang | - |
dc.identifier.doi | 10.1007/s11128-014-0895-7 | - |
dc.identifier.wosid | 000349377900001 | - |
dc.identifier.bibliographicCitation | QUANTUM INFORMATION PROCESSING, v.14, no.3, pp.801 - 811 | - |
dc.relation.isPartOf | QUANTUM INFORMATION PROCESSING | - |
dc.citation.title | QUANTUM INFORMATION PROCESSING | - |
dc.citation.volume | 14 | - |
dc.citation.number | 3 | - |
dc.citation.startPage | 801 | - |
dc.citation.endPage | 811 | - |
dc.type.rims | ART | - |
dc.type.docType | Article | - |
dc.description.journalClass | 1 | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.relation.journalResearchArea | Physics | - |
dc.relation.journalWebOfScienceCategory | Quantum Science & Technology | - |
dc.relation.journalWebOfScienceCategory | Physics, Multidisciplinary | - |
dc.relation.journalWebOfScienceCategory | Physics, Mathematical | - |
dc.subject.keywordAuthor | Quantum knot | - |
dc.subject.keywordAuthor | Knot mosaic | - |
dc.subject.keywordAuthor | Enumeration | - |
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