It was recently shown that, taking into account the granular structure of graphene lattice, the Dirac-like dynamics of its quasiparticles resists beyond the lowest energy approximation. This can be described in terms of new phase-space variables, , that enjoy generalized Heisenberg algebras. In this letter, we add to that picture the important case of noncommuting , for which and we find that , with ℓ the lattice spacing. We close by giving both the general recipe and a possible specific kinematic setup for the practical implementation of this approach to test noncommutative theories in tabletop analog experiments on graphene.
{ "license": [ { "url": "http://creativecommons.org/licenses/by/3.0/", "license": "CC-BY-3.0" } ], "copyright": [ { "holder": "The Author(s)", "statement": "The Author(s)", "year": "2024" } ], "control_number": "84594", "_oai": { "updated": "2024-04-25T09:31:46Z", "id": "oai:repo.scoap3.org:84594", "sets": [ "PLB" ] }, "authors": [ { "surname": "Iorio", "given_names": "Alfredo", "affiliations": [ { "country": "Czech Republic", "value": "Faculty of Mathematics and Physics, Charles University, V Hole\u0161ovi\u010dk\u00e1ch 2, Prague 8, Czech Republic" } ], "full_name": "Iorio, Alfredo", "orcid": "0000-0002-1411-2404", "email": "iorio@matfyz.cuni.cz" }, { "surname": "Iveti\u0107", "given_names": "Boris", "affiliations": [ { "country": "Austria", "value": "W\u00f6hlergasse 6, Vienna, Austria" } ], "full_name": "Iveti\u0107, Boris", "orcid": "0000-0002-6076-3179", "email": "bivetic@yahoo.com" }, { "surname": "Pais", "given_names": "Pablo", "affiliations": [ { "country": "Chile", "value": "Instituto de Ciencias F\u00edsicas y Matem\u00e1ticas, Universidad Austral de Chile, Casilla 567, Valdivia, Chile" }, { "country": "Czech Republic", "value": "Faculty of Mathematics and Physics, Charles University, V Hole\u0161ovi\u010dk\u00e1ch 2, Prague 8, Czech Republic" } ], "full_name": "Pais, Pablo", "orcid": "0000-0002-9320-3223", "email": "pais@matfyz.cuni.cz" } ], "_files": [ { "checksum": "md5:7fc3de990c2b162aa955aaba2e95077f", "filetype": "xml", "bucket": "73cea20c-7a35-41d9-a79c-d4ea627675fc", "version_id": "7ce1fc1a-e19e-4c22-86b3-7ca38665297e", "key": "10.1016/j.physletb.2024.138630.xml", "size": 165044 }, { "checksum": "md5:ab69fbfe6f888322f73c1e48f276dbf8", "filetype": "pdf", "bucket": "73cea20c-7a35-41d9-a79c-d4ea627675fc", "version_id": "d9e99e31-7e22-42db-9513-95ad73ef6821", "key": "10.1016/j.physletb.2024.138630.pdf", "size": 486691 } ], "record_creation_date": "2024-04-10T21:30:29.284510", "titles": [ { "source": "Elsevier", "title": "Turning graphene into a lab for noncommutativity" } ], "collections": [ { "primary": "Physics Letters B" } ], "dois": [ { "value": "10.1016/j.physletb.2024.138630" } ], "publication_info": [ { "journal_volume": "849 C", "journal_title": "Physics Letters B", "material": "article", "artid": "138630", "year": 2024 } ], "$schema": "http://repo.scoap3.org/schemas/hep.json", "abstracts": [ { "source": "Elsevier", "value": "It was recently shown that, taking into account the granular structure of graphene lattice, the Dirac-like dynamics of its quasiparticles resists beyond the lowest energy approximation. This can be described in terms of new phase-space variables, <math><mo>(</mo><mover><mrow><mi>X</mi></mrow><mrow><mo>\u2192</mo></mrow></mover><mo>,</mo><mover><mrow><mi>P</mi></mrow><mrow><mo>\u2192</mo></mrow></mover><mo>)</mo></math>, that enjoy generalized Heisenberg algebras. In this letter, we add to that picture the important case of noncommuting <math><mover><mrow><mi>X</mi></mrow><mrow><mo>\u2192</mo></mrow></mover></math>, for which <math><mo>[</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msup><mo>,</mo><msup><mrow><mi>X</mi></mrow><mrow><mi>j</mi></mrow></msup><mo>]</mo><mo>=</mo><mi>i</mi><mspace width=\"0.2em\"></mspace><msup><mrow><mi>\u03b8</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msup></math> and we find that <math><msup><mrow><mi>\u03b8</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msup><mo>=</mo><msup><mrow><mi>\u2113</mi></mrow><mrow><mn>2</mn></mrow></msup><mspace width=\"0.2em\"></mspace><msup><mrow><mi>\u03f5</mi></mrow><mrow><mi>i</mi><mi>j</mi></mrow></msup></math>, with \u2113 the lattice spacing. We close by giving both the general recipe and a possible specific kinematic setup for the practical implementation of this approach to test noncommutative theories in tabletop analog experiments on graphene." } ], "imprints": [ { "date": "2024-04-04", "publisher": "Elsevier" } ], "acquisition_source": { "date": "2024-04-25T09:30:45.878609", "source": "Elsevier", "method": "Elsevier", "submission_number": "6323940602e611ef81c58e7301cc4a06" } }