{"id":"https://openalex.org/W4406913878","doi":"https://doi.org/10.3390/sym17020202","title":"Complex Dynamics in Circular and Deformed Bilayer Graphene-Inspired Billiards with Anisotropy and Strain","display_name":"Complex Dynamics in Circular and Deformed Bilayer Graphene-Inspired Billiards with Anisotropy and Strain","publication_year":2025,"publication_date":"2025-01-28","ids":{"openalex":"https://openalex.org/W4406913878","doi":"https://doi.org/10.3390/sym17020202"},"language":"en","primary_location":{"id":"doi:10.3390/sym17020202","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020202","pdf_url":"https://www.mdpi.com/2073-8994/17/2/202/pdf?version=1738053424","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/2/202/pdf?version=1738053424","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023388054","display_name":"Lukas Seemann","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Lukas Seemann","raw_affiliation_strings":["Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012293283","display_name":"Jonathan A. Lukin","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jana Lukin","raw_affiliation_strings":["Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Max H\u00e4\u00dfler","orcid":null},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Max H\u00e4\u00dfler","raw_affiliation_strings":["Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005632579","display_name":"Sibylle Gemming","orcid":"https://orcid.org/0000-0003-0455-1945"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sibylle Gemming","raw_affiliation_strings":["Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069176877","display_name":"Martina Hentschel","orcid":"https://orcid.org/0000-0003-0596-6982"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martina Hentschel","raw_affiliation_strings":["Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Physics, Technische Universit\u00e4t Chemnitz, D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5023388054"],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.6281,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.78531007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"17","issue":"2","first_page":"202","last_page":"202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13261","display_name":"Elasticity and Wave Propagation","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13261","display_name":"Elasticity and Wave Propagation","score":0.9761000275611877,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9437999725341797,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9194999933242798,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.689671516418457},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.6488935947418213},{"id":"https://openalex.org/keywords/strain","display_name":"Strain (injury)","score":0.6040780544281006},{"id":"https://openalex.org/keywords/graphene","display_name":"Graphene","score":0.5783000588417053},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.5689472556114197},{"id":"https://openalex.org/keywords/bilayer","display_name":"Bilayer","score":0.47779354453086853},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4646209180355072},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.43781623244285583},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.38787463307380676},{"id":"https://openalex.org/keywords/nanotechnology","display_name":"Nanotechnology","score":0.25497502088546753},{"id":"https://openalex.org/keywords/membrane","display_name":"Membrane","score":0.13421905040740967},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.11168378591537476},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.0940123200416565},{"id":"https://openalex.org/keywords/anatomy","display_name":"Anatomy","score":0.05253538489341736}],"concepts":[{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.689671516418457},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.6488935947418213},{"id":"https://openalex.org/C2778022156","wikidata":"https://www.wikidata.org/wiki/Q576145","display_name":"Strain (injury)","level":2,"score":0.6040780544281006},{"id":"https://openalex.org/C30080830","wikidata":"https://www.wikidata.org/wiki/Q169917","display_name":"Graphene","level":2,"score":0.5783000588417053},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.5689472556114197},{"id":"https://openalex.org/C192157962","wikidata":"https://www.wikidata.org/wiki/Q4087243","display_name":"Bilayer","level":3,"score":0.47779354453086853},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4646209180355072},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.43781623244285583},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.38787463307380676},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.25497502088546753},{"id":"https://openalex.org/C41625074","wikidata":"https://www.wikidata.org/wiki/Q176088","display_name":"Membrane","level":2,"score":0.13421905040740967},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.11168378591537476},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0940123200416565},{"id":"https://openalex.org/C105702510","wikidata":"https://www.wikidata.org/wiki/Q514","display_name":"Anatomy","level":1,"score":0.05253538489341736},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17020202","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020202","pdf_url":"https://www.mdpi.com/2073-8994/17/2/202/pdf?version=1738053424","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/sym17020202","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17020202","pdf_url":"https://www.mdpi.com/2073-8994/17/2/202/pdf?version=1738053424","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3737004470","display_name":null,"funder_award_id":"FOR 5242","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G378319762","display_name":null,"funder_award_id":"FOR 524","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4550752680","display_name":null,"funder_award_id":"449119662","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8330397625","display_name":null,"funder_award_id":"Funding","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321613","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406913878.pdf","grobid_xml":"https://content.openalex.org/works/W4406913878.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1625339619","https://openalex.org/W1983208977","https://openalex.org/W1990463394","https://openalex.org/W1998727969","https://openalex.org/W2002314648","https://openalex.org/W2023602744","https://openalex.org/W2029123711","https://openalex.org/W2076297931","https://openalex.org/W2085714244","https://openalex.org/W2146823643","https://openalex.org/W2152254020","https://openalex.org/W2179508392","https://openalex.org/W2226855983","https://openalex.org/W2289231535","https://openalex.org/W2320888013","https://openalex.org/W2618049591","https://openalex.org/W2901175744","https://openalex.org/W3036087319","https://openalex.org/W3080130023","https://openalex.org/W3203226244","https://openalex.org/W4232454247","https://openalex.org/W4319077905","https://openalex.org/W4375948354","https://openalex.org/W4392553486","https://openalex.org/W4394718261","https://openalex.org/W4401335942","https://openalex.org/W4401479759","https://openalex.org/W4403087703","https://openalex.org/W4405187033"],"related_works":["https://openalex.org/W2606452130","https://openalex.org/W3149465128","https://openalex.org/W3196929922","https://openalex.org/W2377562106","https://openalex.org/W3103904106","https://openalex.org/W2081887179","https://openalex.org/W4321795992","https://openalex.org/W2328592354","https://openalex.org/W3033906315","https://openalex.org/W1578765583"],"abstract_inverted_index":{"While":[0],"billiard":[1],"systems":[2,12,41,105],"of":[3,16,62,75,83,116,131],"various":[4,63],"shapes":[5],"have":[6,24],"been":[7],"used":[8],"as":[9,133],"paradigmatic":[10],"model":[11],"in":[13,33,102,119],"the":[14,30,73,81,87,114,128],"fields":[15],"nonlinear":[17],"dynamics":[18,89,101,115],"and":[19,35,38,65,99,106,121,127],"quantum":[20],"chaos,":[21],"few":[22],"studies":[23],"investigated":[25],"anisotropic":[26,50,117],"billiards.":[27],"Motivated":[28],"by":[29],"tremendous":[31],"advances":[32],"using":[34,67,124],"controlling":[36],"electronic":[37],"optical":[39],"mesoscopic":[40],"with":[42],"bilayer":[43],"graphene":[44],"(BLG),":[45],"representing":[46],"an":[47],"easily":[48],"accessible":[49],"material":[51],"for":[52],"electrons":[53],"when":[54],"trigonal":[55],"warping":[56],"is":[57],"present,":[58],"we":[59],"investigate":[60],"billiards":[61,118],"anisotropies":[64],"geometries":[66],"a":[68],"trajectory-tracing":[69],"approach":[70],"founded":[71],"on":[72],"concept":[74],"ray\u2013wave":[76],"correspondence.":[77],"We":[78,112],"find":[79],"that":[80],"presence":[82],"anisotropy":[84],"can":[85],"change":[86],"billiards\u2019":[88],"dramatically":[90],"from":[91],"its":[92],"isotropic":[93],"counterpart.":[94],"It":[95],"may":[96,107],"induce":[97],"chaotic":[98],"mixed":[100],"otherwise":[103],"integrable":[104],"stabilize":[108],"originally":[109],"unstable":[110],"trajectories.":[111],"characterize":[113],"real":[120],"phase":[122,134],"space":[123,135],"Lyapunov":[125],"exponents":[126],"Poincar\u00e9":[129],"surface":[130],"section":[132],"representation.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}