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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/34066

Title: Maximal scarring for eigenfunctions of quantum graphs
Authors: Berkolaiko, G.
Winn, Brian
Issue Date: 2018
Publisher: IOP Publishing
Citation: BERKOLAIKO, G. and WINN, B., 2018. Maximal scarring for eigenfunctions of quantum graphs. Nonlinearity, In Press.
Abstract: We prove the existence of scarred eigenstates for star graphs with scattering matrices at the central vertex which are either a Fourier transform matrix, or a matrix that prohibits back-scattering. We prove the existence of scars that are half-delocalised on a single bond. Moreover we show that the scarred states we construct are maximal in the sense that it is impossible to have quantum eigenfunctions with a significantly lower entropy than our examples. These scarred eigenstates are on graphs that exhibit generic spectral statistics of random matrix type in the large graph limit, and, in contrast to other constructions, correspond to non-degenerate eigenvalues; they exist for almost all choices of lengths
Description: This paper is in closed access until 12 months after publication.
Sponsor: GB acknowledges partial support from the NSF under grant DMS1410657.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/34066
Publisher Link: http://iopscience.iop.org/journal/0951-7715
ISSN: 0951-7715
Appears in Collections:Closed Access (Maths)

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