PT Symmetric Schr\"odinger Operators: Reality of the Perturbed Eigenvalues (2010)
Caliceti, Emanuela, Cannata, Francesco, Graffi, Sandro
We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic...
PT Symmetric Schrödinger Operators: Reality of the Perturbed Eigenvalues (2010)
Emanuela Caliceti, Francesco Cannata, Sandro Graffi
We prove the reality of the perturbed eigenvalues of some PT symmetric Hamiltonians of physical interest by means of stability methods. In particular we study 2-dimensional generalized harmonic...
Emanuela Caliceti, Ro Graffi, Johannes Sjöstrand
Consider in L 2 (R d), d ≥ 1, the operator family H(g): = H0 + igW. H0 = a ∗ 1 a1 +...+a ∗ d ad +d/2 is the quantum harmonic oscillator with rational frequencies, W a P symmetric bounded...
Distributional Borel Summability for Vacuum Polarization by an External Electric Field # (2007)
It is proved that the divergent perturbation expansion for the vacuum polarization by an external constant electric field in the pair production sector is Borel summable in the distributional sense....
Spectral theory and distributional Borel summability for the quantum H\'enon-Heiles model (2005)
The Borel summability in the distributional sense is established of the divergent perturbation theory for the ground state resonance of the quantum H\'enon-Heiles model.
Spectra of PT-Symmetric Operators and Perturbation Theory (2004)
Caliceti, Emanuela, Graffi, Sandro, Sjoestrand, Johannes
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 particular discrete...
Construction of PT-asymmetric non-Hermitian Hamiltonians with CPT-symmetry (2004)
Caliceti, Emanuela, Cannata, Francesco, Znojil, Miloslav, Ventura, Alberto
Within CPT-symmetric quantum mechanics the most elementary differential form of the charge operator C is assumed. A closed-form integrability of the related coupled differential self-consistency...
Distributional Borel Summability for Vacuum Polarization by an External Electric Field (2002)
It is proved that the divergent perturbation expansion for the vacuum polarization by an external constant electric field in the pair production sector is Borel summable in the distributional sense.
Distributional Borel Summability of Odd Anharmonic Oscillators (1999)
It is proved that the divergent Rayleigh-Schrodinger perturbation expansions for the eigenvalues of any odd anharmonic oscillator are Borel summable in the distributional sense to the resonances...