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• W2966289670 abstract "Consider a sequence of finite regular graphs converging, in the sense of Benjamini–Schramm, to the infinite regular tree. We study the induced quantum graphs with equilateral edge lengths, Kirchhoff conditions (possibly with a non-zero coupling constant α) and a symmetric potential U on the edges. We show that in the spectral regions where the infinite quantum tree has absolutely continuous spectrum, the eigenfunctions of the converging quantum graphs satisfy a quantum ergodicity theorem. In case α = 0 and U = 0 , the limit measure is the uniform measure on the edges. In general, it has an explicit C 1 density. We finally prove a stronger quantum ergodicity theorem involving integral operators, the purpose of which is to study eigenfunction correlations." @default.
• W2966289670 created "2019-08-13" @default.
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• W2966289670 date "2019-07-26" @default.
• W2966289670 modified "2023-10-06" @default.
• W2966289670 title "Quantum ergodicity for large equilateral quantum graphs" @default.
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• W2966289670 doi "https://doi.org/10.1112/jlms.12259" @default.
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