Consider in $L^2(R^l)$ the operator family $H(epsilon):=P_0(hbar,omega)+epsilon Q_0$. $P_0$ is the quantum harmonic oscillator with diophantine frequency vector $om$, $Q_0$ a bounded pseudodifferential operator with symbol holomorphic and decreasing to zero at infinity, and $epinR$. Then there exists $ep^ast >0$ with the property that if $|ep|
D.Borthwick, S.Graffi (2005). A Local Quantum Version of the Kolmogorov Theorem. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 257, 499-514 [10.1007/s00220-005-1299-4].
A Local Quantum Version of the Kolmogorov Theorem
GRAFFI, SANDRO
2005
Abstract
Consider in $L^2(R^l)$ the operator family $H(epsilon):=P_0(hbar,omega)+epsilon Q_0$. $P_0$ is the quantum harmonic oscillator with diophantine frequency vector $om$, $Q_0$ a bounded pseudodifferential operator with symbol holomorphic and decreasing to zero at infinity, and $epinR$. Then there exists $ep^ast >0$ with the property that if $|ep|File in questo prodotto:
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