Rodnianski, Igor; Schlag, Wilhelm; Soffer, Avraham Dispersive analysis of charge transfer models. (English) Zbl 1130.81053 Commun. Pure Appl. Math. 58, No. 2, 149-216 (2005). 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. Cited in 3 ReviewsCited in 53 Documents 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 Citations:Zbl 0437.47008; Zbl 0741.35050 PDFBibTeX XMLCite \textit{I. Rodnianski} et al., Commun. Pure Appl. Math. 58, No. 2, 149--216 (2005; Zbl 1130.81053) Full Text: DOI arXiv References: [1] Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of N body Schrödinger operators. Mathematical Notes, 29. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1982. · Zbl 0503.35001 [2] Ben-Artzi, J Anal Math 58 pp 25– (1992) [3] Burq, J Funct Anal 203 pp 519– (2003) [4] Buslaev, Algebra i Analiz 4 pp 63– (1992) [5] St Petersburg Math J 4 pp 1111– (1993) [6] Constantin, J Amer Math Soc 1 pp 413– (1988) [7] Constantin, Indiana Univ Math J 38 pp 791– (1989) [8] Cuccagna, Comm Pure Appl Math 54 pp 1110– (2001) [9] Doi, Duke Math J 82 pp 679– (1996) [10] Dolph, J Math Anal Appl 16 pp 311– (1966) [11] ; ; Dynamics of solitons in the nonlinear Hartree equation. Preprint. [12] Personal communication. [13] Ginibre, J Funct Anal 133 pp 50– (1995) [14] Graf, Helv Phys Acta 63 pp 107– (1990) [15] Grill Grillakis, Comm Pure Appl Math 43 pp 299– (1990) [16] Grillakis, J Funct Anal 74 pp 160– (1987) [17] Hu Hunziker, J Mathematical Phys 7 pp 300– (1966) [18] Journé, Comm Pure Appl Math 44 pp 573– (1991) [19] Kato, Rev Math Phys 1 pp 481– (1989) [20] Keel, Amer J Math 120 pp 955– (1998) [21] Nier, J Funct Anal 198 pp 511– (2003) [22] Rauch, Comm Math Phys 61 pp 149– (1978) [23] ; Methods of modern mathematical physics. IV. Analysis of operators. Academic, New York?London, 1979. [24] Rodnianski, Invent Math 155 pp 451– (2004) [25] ; ; Asymptotic stability of N soliton states of NLS. Preprint, 2003. [26] Shatah, Comm Math Phys 100 pp 173– (1985) [27] Sjölin, Duke Math J 55 pp 699– (1987) [28] Soffer, Astérisque 207 pp 109– (1992) [29] On the linear stability of solitary waves in Hamiltonian systems with symmetry. Integrable systems and applications Île d’Oléron, 1988), 328-335. Lecture Notes in Physics, 342. Springer, Berlin, 1989. [30] ; The nonlinear Schrödinger equation. Self-focusing and wave collapse. Applied Mathematical Sciences, 139. Springer, New York, 1999. · Zbl 0928.35157 [31] Pseudodifferential operators. Princeton Mathematical Series, 34. Princeton University Press, Princeton, N.J., 1981. [32] Va?? nberg, Uspehi Mat Nauk 30 pp 3– (1975) [33] Vega, Proc Amer Math Soc 102 pp 874– (1988) [34] Weder, J Funct Anal 170 pp 37– (2000) [35] Weinstein, SIAM J Math Anal 16 pp 472– (1985) [36] Weinstein, Comm Math Phys 180 pp 389– (1996) [37] Wüller, Duke Math J 62 pp 273– (1991) [38] Yajima, Comm Math Phys 75 pp 153– (1980) [39] Yajima, J Math Soc Japan 47 pp 551– (1995) [40] Yajima, Comm Math Phys 208 pp 125– (1999) [41] Zielinski, J Funct Anal 150 pp 453– (1997) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.