A uniform quantum version of the Cherry theorem
| dc.creator | Blas, Carlos Villegas | |
| dc.creator | Graffi, Sandro | |
| dc.date | 2007-02-08 | |
| dc.date.accessioned | 2026-07-07T07:45:32Z | |
| dc.date.available | 2026-07-07T07:45:32Z | |
| dc.description | Consider in $L^2(\R^2)$ the operator family $H(ε):=P_0(\hbar,ω)+εF_0$. $P_0$ is the quantum harmonic oscillator with diophantine frequency vector $\om$, $F_0$ a bounded pseudodifferential operator with symbol decreasing to zero at infinity in phase space, and $\ep\in\C$. Then there exist $\ep^\ast >0$ independent of $\hbar$ and an open set $Ω\subset\C^2\setminus\R^2$ such that if $|\ep|<\ep^\ast$ and $\om\in\Om$ the quantum normal form near $P_0$ converges uniformly with respect to $\hbar$. This yields an exact quantization formula for the eigenvalues, and for $\hbar=0$ the classical Cherry theorem on convergence of Birkhoff's normal form for complex frequencies is recovered. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0702021 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0702021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123557 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 81S30; 70H08 | |
| dc.title | A uniform quantum version of the Cherry theorem | |
| dc.type | text |