{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,28]],"date-time":"2026-07-28T19:27:52Z","timestamp":1785266872683,"version":"3.55.0"},"reference-count":50,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T00:00:00Z","timestamp":1702944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The theory of open quantum systems is applied to study galvano-, thermo-magnetic, and magnetization phenomena in axial symmetric two-dimensional systems. Charge carriers are considered as quantum particles interacting with the environment through a one-body (mean-field) mechanism. The dynamics of charge carriers is affected by the average collision time that takes effectively into account two-body effects. The functional dependencies of the average collision time on the external uniform magnetic field, concentration and temperature are phenomenologically treated. Analytical expressions are obtained for the tensors of electric and thermal conductivity and\/or resistivity. The developed theory is applied to describe the Shubnikov-de Haas oscillations and quantum Hall effect in graphene and GaAs\/AlxGa1\u2212xAs heterostructure. The dependencies of magnetization and thermal conductivity on the magnetic field are also predicted.<\/jats:p>","DOI":"10.3390\/sym16010007","type":"journal-article","created":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T11:17:24Z","timestamp":1702984644000},"page":"7","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Quantum Hall and Shubnikov-de Haas Effects in Graphene within Non-Markovian Langevin Approach"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4071-9215","authenticated-orcid":false,"given":"Erkin Kh.","family":"Alpomishev","sequence":"first","affiliation":[{"name":"Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia"},{"name":"Institute of Nuclear Physics, Tashkent 100214, Uzbekistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gurgen G.","family":"Adamian","sequence":"additional","affiliation":[{"name":"Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3666-3389","authenticated-orcid":false,"given":"Nikolay V.","family":"Antonenko","sequence":"additional","affiliation":[{"name":"Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia"},{"name":"Tomsk Polytechnic University, 634050 Tomsk, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1530","DOI":"10.1126\/science.1158877","article-title":"Graphene: Status and Prospects","volume":"324","author":"Geim","year":"2009","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1103\/RevModPhys.83.837","article-title":"Nobel Lecture: Graphene: Materials in the Flatland","volume":"83","author":"Novoselov","year":"2011","journal-title":"Phys. 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