{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1360848659384201216.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.1088/1751-8121/aaa08e"}},{"identifier":{"@type":"URI","@value":"http://stacks.iop.org/1751-8121/51/i=5/a=053002?key=crossref.eefda0fd15910758164a0faa37853efd"}},{"identifier":{"@type":"URI","@value":"http://iopscience.iop.org/article/10.1088/1751-8121/aaa08e/pdf"}},{"identifier":{"@type":"URI","@value":"http://stacks.iop.org/1751-8121/51/i=5/a=053002/pdf"}},{"identifier":{"@type":"URI","@value":"http://iopscience.iop.org/article/10.1088/1751-8121/aaa08e"}},{"identifier":{"@type":"DOI","@value":"10.48550/arxiv.1610.06925"}}],"resourceType":"学術雑誌論文(journal article)","dc:title":[{"@value":"Quantum trilogy: discrete Toda, Y-system and chaos"}],"description":[{"notation":[{"@value":"We discuss a discretization of the quantum Toda field theory associated with a semisimple finite-dimensional Lie algebra or a tamely-laced infinite-dimensional Kac-Moody algebra $G$, generalizing the previous construction of discrete quantum Liouville theory for the case $G=A_1$. The model is defined on a discrete two-dimensional lattice, whose spatial direction is of length $L$. In addition we also find a \"discretized extra dimension\" whose width is given by the rank $r$ of $G$, which decompactifies in the large $r$ limit. For the case of $G=A_N$ or $A_{N-1}^{(1)}$, we find a symmetry exchanging $L$ and $N$ under appropriate spatial boundary conditions. The dynamical time evolution rule of the model is a quantizations of the so-called Y-system, and the theory can be well-described by the quantum cluster algebra. We discuss possible implications for recent discussions of quantum chaos, and comment on the relation with the quantum higher Teichmuller theory of type $A_N$."}]},{"notation":[{"@value":"35 pages, 15 figures; v2: journal version"}]}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1420845751157766400","@type":"Researcher","personIdentifier":[{"@type":"KAKEN_RESEARCHERS","@value":"00726599"},{"@type":"NRID","@value":"1000000726599"},{"@type":"NRID","@value":"9000239558940"},{"@type":"NRID","@value":"9000018481391"},{"@type":"NRID","@value":"9000351492283"},{"@type":"RESEARCHMAP","@value":"https://researchmap.jp/masahito"}],"foaf:name":[{"@value":"Masahito Yamazaki"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"17518113"},{"@type":"EISSN","@value":"17518121"}],"prism:publicationName":[{"@value":"Journal of Physics A: Mathematical and Theoretical"}],"dc:publisher":[{"@value":"IOP Publishing"}],"prism:publicationDate":"2018-01-04","prism:volume":"51","prism:number":"5","prism:startingPage":"053002"},"reviewed":"false","dc:rights":["http://iopscience.iop.org/info/page/text-and-data-mining","http://iopscience.iop.org/page/copyright"],"url":[{"@id":"http://stacks.iop.org/1751-8121/51/i=5/a=053002?key=crossref.eefda0fd15910758164a0faa37853efd"},{"@id":"http://iopscience.iop.org/article/10.1088/1751-8121/aaa08e/pdf"},{"@id":"http://stacks.iop.org/1751-8121/51/i=5/a=053002/pdf"},{"@id":"http://iopscience.iop.org/article/10.1088/1751-8121/aaa08e"}],"createdAt":"2017-12-11","modifiedAt":"2020-04-11","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=High%20Energy%20Physics%20-%20Theory","dc:title":"High Energy Physics - Theory"},{"@id":"https://cir.nii.ac.jp/all?q=Statistical%20Mechanics%20(cond-mat.stat-mech)","dc:title":"Statistical Mechanics (cond-mat.stat-mech)"},{"@id":"https://cir.nii.ac.jp/all?q=FOS:%20Physical%20sciences","dc:title":"FOS: Physical 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