Spectral analysis for \(N\)-particle systems with Stark effect: Nonexistence of bound states and principle of limiting absorption (Q1890831)

The local commutator method has been initiated by \textit{E. Mourre} [Commun. Math. Phys. 78, 391-408 (1981; Zbl 0489.47010)] and major progress has been made in the spectral and scattering theory for many-particle Schrödinger operators during the last decade. By making use of this method, for example, the principle of limiting absorption has been established and the nonexistence of positive eigenvalues has been proved. Furthermore, it has also played a basic role in proving the asymptotic completeness of wave operators. In this work, we use this remarkable method to prove the nonexistence of bound states and the principle of limiting absorption for many-particle Stark Hamiltonians with homogeneous electric fields. The results obtained have an important application to the problem on the asymptotic completeness of wave operators.