124 citations · 452 across the 28 of their papers we have counts for
28 papers
Convergent Quantum Normal Forms, -symmetry and reality of the spectrum
Emanuela Caliceti, Sandro Graffi
A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is expl…
Quadratic PT-symmetric operators with real spectrum and similarity to self-adjoint operators
Emanuela Caliceti, Sandro Graffi, Michael Hitrik +1
It is established that a PT-symmetric elliptic quadratic differential operator with real spectrum is similar to a self-adjoint operator precisely when the associated fundamental ma…
Convergence of a quantum normal form and an exact quantization formula
Sandro Graffi, Thierry Paul
We consider the Schrödinger operator defined by the quantization of the linear flow of diophantine frequencies over the l-dimensional torus, perturbed by a holomorphic potential wh…
Geometric approach to the Hamilton-Jacobi equation and global parametrices for the Schrödinger propagator
Sandro Graffi, Lorenzo Zanelli
We construct a family of Fourier Integral Operators, defined for arbitrary large times, representing a global parametrix for the Schrödinger propagator when the potential is quadra…
Classical limit of the quantum Zeno effect
Paolo Facchi, Sandro Graffi, Marilena Ligabò
The evolution of a quantum system subjected to infinitely many measurements in a finite time interval is confined in a proper subspace of the Hilbert space. This phenomenon is call…
A criterion for the reality of the spectrum of PT symmetric Schroedinger operators with complex-valued periodic potentials
E. Caliceti, S. Graffi
Consider in the \Sc operator family depending on the real parameter , where is a complex-valued but symmetric periodic potential. A…