S. Graffi

activity

19942012

most citedTime Quasi-periodic unbounded perturbations of Schrödinger operators and KAM methods

124 citations · 452 across the 28 of their papers we have counts for

collaborators

Showing 2004 · math-phShow all

3 papers · 2 filters

math-ph2004★ 64 cited

Spectra of PT-Symmetric Operators and Perturbation Theory

Emanuela Caliceti, Sandro Graffi, Johannes Sjoestrand

Criteria are formulated both for the existence and for the non-existence of complex eigenvalues for a class of non self-adjoint operators in Hilbert space invarariant under a parti…

math-ph2004★ 1 cited

A local quantum version of the Kolmogorov theorem

D. Borthwick, S. Graffi

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 $\om$, $Q_{0}$ a bounded pseudodiff…

math-ph2004★ 3 cited

Canonical Expansion of PT-Symmetric Operators and Perturbation Theory

E. Caliceti, S. Graffi

Let $H$ be any $\PT$ symmetric Schrödinger operator of the type $- ℏ^{2} Δ + (x_{1}^{2} + ... + x_{d}^{2}) + i g W (x_{1}, ..., x_{d})$ on $L^{2} (R^{d})$ , where $W$ is any odd homogeneous polynomial and $g\i…