Spectral and scattering theory for 3-particle Hamiltonian with Stark effect : Non-existence of bound states and resolvent estimate

Abstract

The present work is a continuation to [16], in which the author has proved the asymptotic completeness of wave operators for three-particle Stark Hamiltonians. In the proof there, the following two results about the spectral properties of two-particle subsystem Hamiltonians have played a central role: (1) non-existence of bound states; (2) uniform resolvent estimate at high energies. We here consider these two problems for three-particle systems and apply the obtained results to prove the asymptotic completeness for four-particle Stark Hamiltonians under the main assumption that any subsystem Hamiltonian does not have zero reduced charge.