Publication:
Bloch waves and non-commutative tori of magnetic translations

dc.contributor.coauthorPopov, T.
dc.contributor.departmentDepartment of Physics
dc.contributor.kuauthorDereli, Tekin
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T13:19:06Z
dc.date.issued2021
dc.description.abstractWe review the Landau problem of an electron in a constant uniform magnetic field. The magnetic translations are the invariant transformations of the free Hamiltonian. A Kähler polarization of the plane has been used for the geometric quantization. Under the assumption of quasi-periodicity of the wavefunction, the Zak's magnetic translations in the Bravais lattice generate a non-commutative quantum torus. We concentrate on the case when the magnetic flux density is a rational number. The Bloch wavefunctions form a finite-dimensional module of the noncommutative torus of magnetic translations as well as of its commutant, which is the non-commutative torus of magnetic translations in the dual Bravais lattice. The bi-module structure of the Bloch waves is shown to be the connecting link between two Morita equivalent non-commutative tori. The main focus of our review is the Kähler structure on the Hilbert space of Bloch waves and its inherent quantum toric geometry. We reveal that the metaplectic group Mp(2,R) of the automorphisms of magnetic translation algebras is represented by the quantum optics squeezing operators.
dc.description.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.issue10
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuTÜBİTAK
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TÜBİTAK)
dc.description.sponsorshipBulgarian National Science Fund Research
dc.description.sponsorshipTurkish Academy of Sciences
dc.description.versionPublisher version
dc.description.volume62
dc.identifier.doi10.1063/5.0063174
dc.identifier.eissn1089-7658
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR03486
dc.identifier.issn0022-2488
dc.identifier.quartileN/A
dc.identifier.scopus2-s2.0-85117141775
dc.identifier.urihttps://doi.org/10.1063/5.0063174
dc.identifier.wos755638500004
dc.keywordsInstantons
dc.keywordsYang-mills equation
dc.keywordsSelf-duality
dc.language.isoeng
dc.publisherAmerican Institute of Physics (AIP) Publishing
dc.relation.grantnoDN 18/3
dc.relation.ispartofJournal of Mathematical Physics
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/10278
dc.subjectPhysics
dc.titleBloch waves and non-commutative tori of magnetic translations
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorDereli, Dündar Tekin
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Physics
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