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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Tuan Duong, Anh (2012)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 81Q20 (35P25, 81V10). The purpose of this paper is to study the Schrödinger operator P(B,w) = (Dx-By^2+Dy^2+w^2x^2+V(x,y),(x,y) О R^2, with the magnetic field B large enough and the constant w № 0 is fixed and proportional to the strength of the electric field. Under certain assumptions on the potential V, we prove the existence of resonances near Landau levels as B®Ґ. Moreover, we show that the width of resonances is of size O(B^-Ґ). ...
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 ...
B. Helffer, J. Sjöstrand (1989)
Recherche Coopérative sur Programme n°25
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J. Bourgain (1996)
Geometric and functional analysis
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Marek Burnat, Jan Herczyński, Bogdan Zawisza (1987)
Banach Center Publications
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Udrişte, C., Balan, V., Udrişte, A. (1999)
APPS. Applied Sciences
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Victor Ivrii (2006-2007)
Séminaire Équations aux dérivées partielles
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I study the Schrödinger operator with the strong magnetic field, considering links between geometry of magnetic field, classical and quantum dynamics associated with operator and spectral asymptotics. In particular, I will discuss the role of short periodic trajectories.
Bernard Helffer, Heinz Siedentop (1995)
Mathematische Zeitschrift
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G. Nakamura, Z. Sun, G. Uhlmann (1995)
Mathematische Annalen
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