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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/18694

Title: Quantum ergodicity for quantum graphs without back-scattering
Authors: Brammall, Matthew
Winn, Brian
Issue Date: 2016
Publisher: © Springer
Citation: BRAMMALL, M. and WINN, B., 2016. Quantum ergodicity for quantum graphs without back-scattering. Annales Henri Poincare. 17(6), pp.1353-1382.
Abstract: We give an estimate of the quantum variance for d-regular graphs quantised with boundary scattering matrices that prohibit back-scattering. For families of graphs that are expanders, with few short cycles, our estimate leads to quantum ergodicity for these families of graphs. Our proof is based on a uniform control of an associated random walk on the bonds of the graph. We show that recent constructions of Ramanujan graphs, and asymptotically almost surely, random d-regular graphs, satisfy the necessary conditions to conclude that quantum ergodicity holds.
Description: The final publication is available at Springer via http://dx.doi.org/10.1007/s00023-015-0435-8
Sponsor: This paper has been supported by EPSRC under grant numbers EP/H046240/1 and EP/I038217/1.
Version: Accepted for publication
DOI: 10.1007/s00023-015-0435-8
URI: https://dspace.lboro.ac.uk/2134/18694
Publisher Link: http://dx.doi.org/10.1007/s00023-015-0435-8
ISSN: 1424-0661
Appears in Collections:Published Articles (Maths)

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