On Reducibility of Schrödinger Equations with Quasiperiodic in Time Potentials

On Reducibility of Schrödinger Equations with Quasiperiodic in Time Potentials

We prove that a linear d -dimensional Schrödinger equation with an x -periodic and t -quasiperiodic potential reduces to an autonomous equation for most values of the frequency vector. The reduction is made by means of a non-autonomous linear transformation of the space of x -periodic functions. Thi...

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Veröffentlicht in:Communications in mathematical physics 2009-02, Vol.286 (1), p.125-135
Hauptverfasser: Eliasson, Håkan L., Kuksin, Sergei B.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis of PDEs
Classical and Quantum Gravitation
Complex Systems
Exact sciences and technology
Functional analysis
Mathematical analysis
Mathematical and Computational Physics
Mathematical methods in physics
Mathematical Physics
Mathematics
Other topics in mathematical methods in physics
Partial differential equations
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Sciences and techniques of general use
Theoretical
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Zusammenfassung:We prove that a linear d -dimensional Schrödinger equation with an x -periodic and t -quasiperiodic potential reduces to an autonomous equation for most values of the frequency vector. The reduction is made by means of a non-autonomous linear transformation of the space of x -periodic functions. This transformation is a quasiperiodic function of t .
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-008-0683-2