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Dispersive analysis of charge transfer models. (English) Zbl 1130.81053

Summary: We prove dispersive estimates for the time-dependent Schrödinger equation with a charge transfer Hamiltonian. As a by-product we also obtain another proof of asymptotic completeness of the wave operators for a charge transfer model established earlier by K. Yajima [Commun. Math. Phys. 75, 153–178 (1980; Zbl 0437.47008)] and G. M. Graf [Helv. Phys. Acta 63, No. 1-2, 107–138 (1990; Zbl 0741.35050)]. We also consider a more general matrix non-self-adjoint charge transfer problem. This model appears naturally in the study of nonlinear multisoliton systems and is specifically motivated by the problem of asymptotic stability of multisoliton states of a nonlinear Schrödinger equation.

MSC:

81U05 \(2\)-body potential quantum scattering theory
35B40 Asymptotic behavior of solutions to PDEs
35Q40 PDEs in connection with quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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