A family of complex potentials with real spectrum

We consider a two-parameter non hermitean quantum-mechanical hamiltonian that is invariant under the combined effects of parity and time reversal transformation. Numerical investigation shows that for some values of the potential parameters the hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other PT symmetric models, which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.Comment: Six figures and four table

Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Schroedinger equation H \psi=E \psi with PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i \beta x^3 +c x^2+i \delta x = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of this non-variational construction is given. Our Taylor series form of \psi complements and completes the recent terminating solutions as obtained for certain couplings \delta at the less common negative a.Comment: 18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appea

Large-scale slope instability affecting SS63 near the Cerreto Pass (northern Apennines, Italy)

National Road SS63 is endangered by large scale slope instability phenomena few km north of the Cerreto Pass (northern Apennines, Italy). At the Col Piagneto slope, SS63 was closed two times in the past 50 years after landslide events. In 1974, the collapse of portion of a rock slide triggered a debris slide that buried more than 50 m of the road track. In 2008, the reactivation of an earth slide in eastern portion of the slope damaged about 400 m of the “new” track built to by-pass the 1974 risk area. In order to evaluate if it is worthwhile keeping the old track open to traffic, or it is maybe better to repair the new track a comprehensive study was financed by Emilia Romagna Region. Research methods included: high resolution DEM, landslides mapping, continuous displacement and groundwater monitoring. Results allowed to assess different semi-quantitative risk scenario for the road structures or vehicles