{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:55:10Z","timestamp":1777449310828,"version":"3.51.4"},"reference-count":42,"publisher":"SAGE Publications","issue":"3-4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ASY"],"published-print":{"date-parts":[[2016,2,12]]},"DOI":"10.3233\/asy-151338","type":"journal-article","created":{"date-parts":[[2016,2,18]],"date-time":"2016-02-18T08:27:04Z","timestamp":1455784024000},"page":"251-281","source":"Crossref","is-referenced-by-count":3,"title":["Bound states in waveguides with complex Robin boundary conditions"],"prefix":"10.1177","volume":"96","author":[{"given":"Radek","family":"Nov\u00e1k","sequence":"first","affiliation":[{"name":"Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, B\u0159ehov\u00e1 7, 115 19, Prague, Czech Republic"},{"name":"Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences of the Czech Republic, Hlavn\u00ed 130, 250 68 \u0158e\u017e near Prague, Czech Republic. E-mail:\u00a0novakra9@fjfi.cvut.cz"}]}],"member":"179","reference":[{"key":"10.3233\/ASY-151338_ref1","unstructured":"[1]M.\u00a0Abramowitz and I.A.\u00a0Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th Dover printing, 10th GPO printing edn, Dover, New York, 1964."},{"key":"10.3233\/ASY-151338_ref2","unstructured":"[2]R.A.\u00a0Adams, Sobolev Spaces, Academic Press, New York, 1975."},{"key":"10.3233\/ASY-151338_ref3","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1088\/0034-4885\/70\/6\/R03","article-title":"Making sense of non-Hermitian Hamiltonians","volume":"70","author":"Bender","year":"2007","journal-title":"Reports on Progress in Physics"},{"key":"10.3233\/ASY-151338_ref4","doi-asserted-by":"crossref","first-page":"5243","DOI":"10.1103\/PhysRevLett.80.5243","article-title":"Real spectra in non-Hermitian Hamiltonians having PT symmetry","volume":"80","author":"Bender","year":"1998","journal-title":"Physical Review Letters"},{"key":"10.3233\/ASY-151338_ref5","first-page":"127","article-title":"On the spectrum of singular boundary-value problems","volume":"55","author":"Birman","year":"1961","journal-title":"Matematicheskii Sbornik"},{"issue":"1","key":"10.3233\/ASY-151338_ref6","doi-asserted-by":"crossref","first-page":"29","DOI":"10.13108\/2014-6-1-29","article-title":"Discrete spectrum of thin PT-symmetric waveguide","volume":"6","author":"Borisov","year":"2014","journal-title":"Ufa Mathematical Journal"},{"issue":"2","key":"10.3233\/ASY-151338_ref7","doi-asserted-by":"crossref","first-page":"93","DOI":"10.14311\/AP.2014.54.0093","article-title":"Eigenvalues collision for PT-symmetric waveguide","volume":"54","author":"Borisov","year":"2014","journal-title":"Acta Polytechnica"},{"issue":"3","key":"10.3233\/ASY-151338_ref8","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/PL00001045","article-title":"Bound states in weakly deformed strips and layers","volume":"2","author":"Borisov","year":"2001","journal-title":"Annales Henri Poincar\u00e9"},{"issue":"4","key":"10.3233\/ASY-151338_ref9","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s00020-008-1634-1","article-title":"PT-symmetric waveguides","volume":"62","author":"Borisov","year":"2008","journal-title":"Integral Equations and Operator Theory"},{"issue":"1","key":"10.3233\/ASY-151338_ref10","doi-asserted-by":"crossref","first-page":"49","DOI":"10.3233\/ASY-2011-1061","article-title":"The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions","volume":"76","author":"Borisov","year":"2012","journal-title":"Asymptotic Anal."},{"issue":"2","key":"10.3233\/ASY-151338_ref11","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1112\/plms\/pdt035","article-title":"Sectorial perturbations of self-adjoint matrices and operators","volume":"108","author":"Davies","year":"2014","journal-title":"Proceedings of the London Mathematical Society"},{"key":"10.3233\/ASY-151338_ref12","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1088\/0305-4470\/34\/1\/304","article-title":"Bounds on complex eigenvalues and resonances","volume":"34","author":"Davies","year":"2001","journal-title":"Journal of Physics A"},{"issue":"8","key":"10.3233\/ASY-151338_ref13","doi-asserted-by":"crossref","first-page":"3892","DOI":"10.1063\/1.1491597","article-title":"Bound states in straight quantum waveguides with combined boundary conditions","volume":"43","author":"Dittrich","year":"2002","journal-title":"J. Math. Phys."},{"key":"10.3233\/ASY-151338_ref14","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1142\/S0129055X95000062","article-title":"Curvature-induced bound states in quantum waveguides in two and three dimensions","volume":"7","author":"Duclos","year":"1995","journal-title":"Rev. Math. Phys."},{"key":"10.3233\/ASY-151338_ref15","unstructured":"[15]D.E.\u00a0Edmunds and W.D.\u00a0Evans, Spectral Theory and Differential Operators, Oxford Mathematical Monographs, Oxford Univ. Press, USA, 1987."},{"key":"10.3233\/ASY-151338_ref16","unstructured":"[16]L.C.\u00a0Evans, Partial Differential Equations, AMS, Providence, 1998."},{"key":"10.3233\/ASY-151338_ref18","doi-asserted-by":"crossref","first-page":"2574","DOI":"10.1063\/1.528538","article-title":"Bound states in curved waveguides","volume":"30","author":"Exner","year":"1989","journal-title":"J. Math. Phys."},{"key":"10.3233\/ASY-151338_ref19","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1112\/blms\/bdr008","article-title":"Eigenvalue bounds for Schr\u00f6dinger operators with complex potentials","volume":"43","author":"Frank","year":"2011","journal-title":"Bulletin London Mathematical Society"},{"issue":"4","key":"10.3233\/ASY-151338_ref20","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/s11040-007-9015-6","article-title":"Waveguides with combined Dirichlet and Robin boundary conditions","volume":"9","author":"Freitas","year":"2006","journal-title":"Mathematical Physics, Analysis and Geometry"},{"key":"10.3233\/ASY-151338_ref21","doi-asserted-by":"crossref","first-page":"14100","DOI":"10.1103\/PhysRevB.45.14100","article-title":"Bound states in twisting tubes","volume":"45","author":"Goldstone","year":"1992","journal-title":"Phys. Rev. B"},{"key":"10.3233\/ASY-151338_ref22","doi-asserted-by":"crossref","first-page":"2149","DOI":"10.1016\/j.physleta.2011.04.021","article-title":"Perfect transmission scattering as a PT-symmetric spectral problem","volume":"375","author":"Hernandez-Coronado","year":"2011","journal-title":"Physics Letters A"},{"key":"10.3233\/ASY-151338_ref23","doi-asserted-by":"crossref","unstructured":"[23]N.\u00a0Hurt, Mathematical Physics of Quantum Wires and Devices: From Spectral Resonances to Anderson Localization, Mathematics and Its Applications, Springer, 2000.","DOI":"10.1007\/978-94-015-9626-8_6"},{"key":"10.3233\/ASY-151338_ref24","doi-asserted-by":"crossref","first-page":"2921","DOI":"10.1090\/S0002-9947-2014-06432-5","article-title":"Non-self-adjoint graphs","volume":"367","author":"Hussein","year":"2015","journal-title":"Trans. Amer. Math. Soc."},{"key":"10.3233\/ASY-151338_ref25","doi-asserted-by":"crossref","unstructured":"[25]J\u00edlek and M.\u00a0Straight, Quantum waveguide with Robin boundary conditions, in: Proceedings of Micro-Conference \u201cAnalytic and Algebraic Methods III\u201d, 2007.","DOI":"10.3842\/SIGMA.2007.108"},{"key":"10.3233\/ASY-151338_ref26","doi-asserted-by":"crossref","first-page":"5325","DOI":"10.1063\/1.1507825","article-title":"Density and current of a dissipative schr\u00f6dinger operator","volume":"43","author":"Kaiser","year":"2002","journal-title":"Journal of Mathematical Physics"},{"issue":"1","key":"10.3233\/ASY-151338_ref27","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/BF02789593","article-title":"Macroscopic current induced boundary conditions for Schr\u00f6dinger-type operators","volume":"45","author":"Kaiser","year":"2003","journal-title":"Integral Equations and Operator Theory"},{"key":"10.3233\/ASY-151338_ref28","doi-asserted-by":"crossref","unstructured":"[28]T.\u00a0Kato, Perturbation Theory for Linear Operators, Springer, 1966.","DOI":"10.1007\/978-3-662-12678-3"},{"key":"10.3233\/ASY-151338_ref29","first-page":"49","article-title":"Some applications of the Birman\u2013Schwinger principle","volume":"55","author":"Klaus","year":"1982","journal-title":"Helvetica Physica Acta"},{"key":"10.3233\/ASY-151338_ref30","doi-asserted-by":"crossref","unstructured":"[30]D.\u00a0Krej\u010di\u0159\u00edk, Calculation of the metric in the Hilbert space of a PT-symmetric model via the spectral theorem, Journal of Physics A: Mathematical and Theoretical 41 (2008), 244012.","DOI":"10.1088\/1751-8113\/41\/24\/244012"},{"key":"10.3233\/ASY-151338_ref31","doi-asserted-by":"crossref","first-page":"10143","DOI":"10.1088\/0305-4470\/39\/32\/S15","article-title":"Closed formula for the metric in the Hilbert space of a PT-symmetric model","volume":"39","author":"Krej\u010di\u0159\u00edk","year":"2006","journal-title":"Journal of Physics A: Mathematical and General"},{"key":"10.3233\/ASY-151338_ref32","doi-asserted-by":"crossref","unstructured":"[32]D.\u00a0Krej\u010di\u0159\u00edk and P.\u00a0Siegl, PT-symmetric models in curved manifolds, Journal of Physics A: Mathematical and Theoretical 43(48) (2010), 485204.","DOI":"10.1088\/1751-8113\/43\/48\/485204"},{"key":"10.3233\/ASY-151338_ref33","doi-asserted-by":"crossref","unstructured":"[33]D.\u00a0Krej\u010di\u0159\u00edk and P.\u00a0Siegl, On the metric operator for the imaginary cubic oscillator, Phys. Rev. D 86 (2012), 121702.","DOI":"10.1103\/PhysRevD.86.121702"},{"key":"10.3233\/ASY-151338_ref35","doi-asserted-by":"crossref","unstructured":"[35]D.\u00a0Krej\u010di\u0159\u00edk and M.\u00a0Tater, Non-Hermitian spectral effects in a PT-symmetric waveguide, Journal of Physics A: Mathematical and Theoretical 41 (2008), 244013.","DOI":"10.1088\/1751-8113\/41\/24\/244013"},{"key":"10.3233\/ASY-151338_ref36","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1007\/s00220-009-0883-4","article-title":"Eigenvalue estimates for Schr\u00f6dinger operators with complex potentials","volume":"292","author":"Laptev","year":"2009","journal-title":"Comm. Math. Phys."},{"key":"10.3233\/ASY-151338_ref37","unstructured":"[37]J.\u00a0Londergan, J.\u00a0Carini and D.\u00a0Murdock, Binding and Scattering in Two-Dimensional Systems: Applications to Quantum Wires, Waveguides and Photonic Crystals, Springer, 1999."},{"key":"10.3233\/ASY-151338_ref38","doi-asserted-by":"crossref","first-page":"1191","DOI":"10.1142\/S0219887810004816","article-title":"Pseudo-Hermitian representation of quantum mechanics","volume":"7","author":"Mostafazadeh","year":"2010","journal-title":"International Journal of Geometric Methods in Modern Physics"},{"issue":"3","key":"10.3233\/ASY-151338_ref39","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1007\/s002200050106","article-title":"Selfadjoint extensions of the Neumann Laplacian in domains with cylindrical outlets","volume":"185","author":"Nazarov","year":"1997","journal-title":"Comm. Math. Phys."},{"key":"10.3233\/ASY-151338_ref40","unstructured":"[40]M.C.\u00a0Reed and B.\u00a0Simon, Analysis of Operators, Methods of Modern Mathematical Physics, Vol.\u00a04, Academic Press, 1978."},{"key":"10.3233\/ASY-151338_ref41","unstructured":"[41]M.C.\u00a0Reed and B.\u00a0Simon, Functional Analysis, Methods of Modern Mathematical Physics, Vol.\u00a01, Academic Press, 1980."},{"key":"10.3233\/ASY-151338_ref42","unstructured":"[42]W.\u00a0Rudin, Real and Complex Analysis, 3rd edn, McGraw-Hill, Inc., New York, NY, USA, 1987."},{"key":"10.3233\/ASY-151338_ref43","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1073\/pnas.47.1.122","article-title":"On the bound states of a given potential","volume":"47","author":"Schwinger","year":"1961","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"key":"10.3233\/ASY-151338_ref44","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/0003-4916(76)90038-5","article-title":"The bound state of weakly coupled Schr\u00f6dinger operators in one and two dimensions","volume":"97","author":"Simon","year":"1976","journal-title":"Annals of Physics"}],"container-title":["Asymptotic Analysis"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/ASY-151338","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:40:43Z","timestamp":1777380043000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.medra.org\/servlet\/aliasResolver?alias=iospress&doi=10.3233\/ASY-151338"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,2,12]]},"references-count":42,"journal-issue":{"issue":"3-4"},"URL":"https:\/\/doi.org\/10.3233\/asy-151338","relation":{},"ISSN":["1875-8576","0921-7134"],"issn-type":[{"value":"1875-8576","type":"electronic"},{"value":"0921-7134","type":"print"}],"subject":[],"published":{"date-parts":[[2016,2,12]]}}}