Periodic Schrödinger Operators with (Non-Periodic) Magnetic and Electric Potentials.
Rainer Hempel (1984)
Manuscripta mathematica
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Rainer Hempel (1984)
Manuscripta mathematica
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M.M. Skriganov (1985)
Inventiones mathematicae
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Jan Herczyński (1987)
Banach Center Publications
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Z. Gan (2010)
Mathematical Modelling of Natural Phenomena
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We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schrödinger operators obtained in ...
H. Krüger (2010)
Mathematical Modelling of Natural Phenomena
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In this note, I wish to describe the first order semiclassical approximation to the spectrum of one frequency quasi-periodic operators. In the case of a sampling function with two critical points, the spectrum exhibits two gaps in the leading order approximation. Furthermore, I will give an example of a two frequency quasi-periodic operator, which has no gaps in the leading order of the semiclassical approximation.
J. Bourgain (1996)
Geometric and functional analysis
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Masahiro Kaminaga (1996)
Forum mathematicum
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Artur Avila, Svetlana Jitomirskaya (2010)
Journal of the European Mathematical Society
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Tatiana Suslina (2000)
Journées équations aux dérivées partielles
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The lecture is devoted to the problem of absolute continuity of the spectrum of periodic operators. A general approach to this problem was suggested by L. Thomas in 1973 for the case of the Schrödinger operator with periodic electric potential. Further application of his method to concrete operators of mathematical physics met analytic difficulties. In recent years several new problems in this area have been solved. We propose a survey of known results in this area, including very recent,...
H. Knörrer, J. Feldman, E. Trubowitz (1990)
Inventiones mathematicae
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