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Endpoint Strichartz estimates for charge transfer Hamiltonians. (English) Zbl 1412.35281

Summary: We prove the optimal Strichartz estimates for Schrödinger equations with charge transfer potentials and general source terms in \(\mathbb{R}^n\) for \(n\geq3\). The proof is based on asymptotic completeness for the charge transfer models and the (weak) point-wise time decay estimates for the scattering states of such systems of I. Rodnianski et al. [Commun. Pure Appl. Math. 58, No. 2, 149–216 (2005; Zbl 1130.81053)]. The method extends for the matrix charge transfer problems.

MSC:

35Q40 PDEs in connection with quantum mechanics
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35B40 Asymptotic behavior of solutions to PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
81U05 \(2\)-body potential quantum scattering theory

Citations:

Zbl 1130.81053
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References:

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