{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:32:27Z","timestamp":1777447947153,"version":"3.51.4"},"reference-count":27,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2019,1,7]],"date-time":"2019-01-07T00:00:00Z","timestamp":1546819200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2019,1,7]]},"abstract":"<jats:p>We consider Dirac, Pauli and Schr\u00f6dinger quantum Hamiltonians with constant magnetic fields of full rank in [Formula: see text], [Formula: see text], perturbed by non-self-adjoint (matrix-valued) potentials. On the one hand, we show the existence of non-self-adjoint perturbations, generating near each point of the essential spectrum of the operators, infinitely many (complex) eigenvalues. On the other hand, we give asymptotic behaviours of the number of the (complex) eigenvalues. In particular, for compactly supported potentials, our results establish non-self-adjoint extensions of Raikov\u2013Warzel [ Rev. in Math. Physics 14 ( 2002 ), 1051\u20131072] and Melgaard\u2013Rozenblum [ Commun. PDE. 28 ( 2003 ), 697\u2013736] results. So, we show how the (complex) eigenvalues converge to the points of the essential spectrum asymptotically, i.e., up to a multiplicative explicit constant, as [Formula: see text] in small annulus of radius [Formula: see text] around the points of the essential spectrum.<\/jats:p>","DOI":"10.3233\/asy-181491","type":"journal-article","created":{"date-parts":[[2019,1,8]],"date-time":"2019-01-08T11:51:10Z","timestamp":1546948270000},"page":"113-136","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Spectral non-self-adjoint analysis of complex Dirac, Pauli and Schr\u00f6dinger operators with constant magnetic fields of full rank"],"prefix":"10.1177","volume":"111","author":[{"given":"Diomba","family":"Sambou","sequence":"first","affiliation":[{"name":"Facultad de Matem\u00e1ticas, Pontificia Universidad Cat\u00f3lica de Chile, Vicu\u00f1a Mackenna 4860, Santiago de Chile, Chile. E-mail:\u00a0"}]}],"member":"179","published-online":{"date-parts":[[2019,1,7]]},"reference":[{"key":"ref001","unstructured":"J.\u00a0Almog, D.S.\u00a0Grebenkov and B.\u00a0Helffer, Spectral semi-classical analysis of a complex Schr\u00f6dinger operator in exterior domains, arXiv:1708.02926."},{"key":"ref002","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-78-04540-4"},{"key":"ref003","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-016-2806-5"},{"key":"ref004","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2013.777453"},{"key":"ref005","doi-asserted-by":"publisher","DOI":"10.1007\/s00023-013-0259-3"},{"key":"ref006","first-page":"317","volume":"3","author":"Dimassi M.","year":"2001","journal-title":"Cubo Matem\u00e1tica Educacional"},{"key":"ref007","unstructured":"C.\u00a0Engstr\u00f6m and A.\u00a0Torshage, Accumulation of complex eigenvalues of a class of analytic operator functions, arXiv:1709.01462."},{"key":"ref008","unstructured":"G.B.\u00a0Folland, Real Analysis Modern Techniques and Their Applications, Pure and Apllied Mathematics, John Whiley and Sons, 1984."},{"key":"ref009","doi-asserted-by":"crossref","unstructured":"I.\u00a0Gohberg, S.\u00a0Goldberg and M.A.\u00a0Kaashoek, Classes of Linear Operators, Operator Theory, Advances and Applications, Vol.\u00a049, Birkh\u00e4user Verlag, 1990.","DOI":"10.1007\/978-3-0348-7509-7_5"},{"key":"ref010","doi-asserted-by":"crossref","unstructured":"I.\u00a0Gohberg, S.\u00a0Goldberg and N.\u00a0Krupnik, Traces and Determinants of Linear Operators, Operator Theory, Advances and Applications, Vol.\u00a0116, Birkh\u00e4user Verlag, 2000.","DOI":"10.1007\/978-3-0348-8401-3"},{"key":"ref011","doi-asserted-by":"crossref","unstructured":"I.\u00a0Gohberg and J.\u00a0Leiterer, Holomorphic Operator Functions of One Variable and Applications, Operator Theory, Advances and Applications, Methods from Complex Analysis in Several Variables, Vol.\u00a0192, Birkh\u00e4user Verlag, 2009.","DOI":"10.1007\/978-3-0346-0126-9"},{"issue":"126","key":"ref012","first-page":"607","volume":"84","author":"Gohberg I.","year":"1971","journal-title":"Mat. 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