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On the Absolutely Continuous Spectrum of Stark Operators.
- Source :
- Communications in Mathematical Physics; Mar2003, Vol. 234 Issue 2, p359-381, 23p
- Publication Year :
- 2003
-
Abstract
- The stability of the absolutely continuous spectrum of the one-dimensional Stark operator H = - <superscript>d²</superscript>/<subscript>dx²</subscript> - Fx, under perturbations of the potential is discussed. The focus is on proving this stability under minimal assumptions on smoothness of the perturbation. A general criterion is presented together with some applications. These include the case of periodic perturbations where we show that any perturbation v &epsiv; L<subscript>1</subscript> (T) ∩ H<superscript>-1/2</superscript>(T) preserves the a.c. spectrum. [ABSTRACT FROM AUTHOR]
- Subjects :
- PERTURBATION theory
OPERATOR theory
FUNCTIONAL analysis
DYNAMICS
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00103616
- Volume :
- 234
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Communications in Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 15732066
- Full Text :
- https://doi.org/10.1007/s00220-002-0776-2