Anomalous real spectra of non-Hermitian quantum graphs in a strong-coupling regime

0346529 - ÚJF 2011 RIV GB eng J - Journal Article
Znojil, Miloslav
Anomalous real spectra of non-Hermitian quantum graphs in a strong-coupling regime.
Journal of Physics A-Mathematical and Theoretical. Roč. 43, č. 33 (2010), 335303/1-335303/14. ISSN 1751-8113. E-ISSN 1751-8121
R&D Projects: GA ČR GA202/07/1307; GA MŠMT LC06002
Institutional research plan: CEZ:AV0Z10480505
Keywords : SYMMETRIC HAMILTONIANS * SPONTANEOUS BREAKDOWN * PERTURBATION-THEORY
Subject RIV: BE - Theoretical Physics
Impact factor: 1.641, year: 2010

A family of one-dimensional quantum systems described by certain weakly non-Hermitian Hamiltonians with real spectra is studied. The presence of a microscopic spatial defect (i.e. of a fundamental length scale theta > 0) is mimicked by the replacement of the real line of coordinates R by a non-tree graph. By construction, this graph only differs from R on a small interval of size O(theta). An unexpected return of the reality of the whole spectrum in an anomalous strong-coupling regime (i.e. the emergence of an isolated island of stability of the system) is then revealed, proved and tentatively attributed to the topological nontriviality of the graph.
Permanent Link: http://hdl.handle.net/11104/0187538