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Research Funding:

Supported in part by NSF grant DMS-0204985

A Local Quantum Version of the Kolmogorov Theorem

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Journal Title:

Communications in Mathematical Physics

Volume:

Volume 257, Number 2

Publisher:

, Pages 499-514

Type of Work:

Article | Final Publisher PDF

Abstract:

Consider in L 2(ℝ l ) the operator family H(ε):=P 0(ℏ,ω)+ε Q 0. P 0 is the quantum harmonic oscillator with diophantine frequency vector ω, Q 0 a bounded pseudodifferential operator with symbol holomorphic and decreasing to zero at infinity, and ε ∈ ℝ. Then there exists ε*>0 with the property that if |ε|<ε* there is a diophantine frequency ω(ε) such that all eigenvalues E n (ℏ,ε) of H(ε) near 0 are given by the quantization formula where α is an l-multi-index.

Copyright information:

© Springer-Verlag 2005

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