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On the location of spectral edges in Z-periodic media
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SYSNO ASEP 0350853 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the location of spectral edges in Z-periodic media Author(s) Exner, Pavel (UJF-V) RID, ORCID, SAI
Kuchment, P. (US)
Winn, B. (GB)Source Title Journal of Physics A-Mathematical and Theoretical. - : Institute of Physics Publishing - ISSN 1751-8113
Roč. 43, č. 47 (2010), 474022/1-474022/8Number of pages 8 s. Language eng - English Country GB - United Kingdom Keywords OPERATORS ; GRAPHS Subject RIV BE - Theoretical Physics R&D Projects LC06002 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10480505 - UJF-V (2005-2011) UT WOS 000284100400023 DOI 10.1088/1751-8113/43/47/474022 Annotation Periodic second-order ordinary differential operators on R are known to have the edges of their spectra to occur only at the spectra of periodic and antiperiodic boundary value problems. The multi-dimensional analog of this property is false, as was shown in a 2007 paper by some of the authors of this paper. However, one sometimes encounters the claims that in the case of a single periodicity (i.e., with respect to the lattice Z), the 1D property still holds, and spectral edges occur at the periodic and anti-periodic spectra only. In this work, we show that even in the simplest case of quantum graphs this is not true. It is shown that this is true if the graph consists of a 1D chain of finite graphs connected by single edges, while if the connections are formed by at least two edges, the spectral edges can already occur away from the periodic and anti-periodic spectra. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2011
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