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Absence of Absolutely Continuous Spectra for Multidimensional Schrödinger Operators with High Barriers
Author(s) -
McGillivray Ivor,
Stollmann Peter,
Stolz Günter
Publication year - 1995
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/27.2.162
Subject(s) - absolute continuity , mathematics , probabilistic logic , pseudodifferential operators , spectrum (functional analysis) , schrödinger's cat , continuous spectrum , spectral line , pure mathematics , mathematical analysis , statistics , quantum mechanics , physics
We prove absence of absolutely continuous spectra for multidimensional Schrödinger operators with high barriers. The result is formulated in terms of a geometric condition on the barriers which entails singular spectrum. The proof combines probabilistic and functional analytic techniques.