Charge transfer scatteringin a constant electric field
Zieliński, Lech
Colloquium Mathematicae, Tome 79 (1999), p. 37-61 / Harvested from The Polish Digital Mathematics Library

We prove the asymptotic completeness of the quantum scattering for a Stark Hamiltonian with a time dependent interaction potential, created by N classical particles moving in a constant electric field.

Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:210626
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     author = {Lech Zieli\'nski},
     title = {Charge transfer scatteringin a constant electric field},
     journal = {Colloquium Mathematicae},
     volume = {79},
     year = {1999},
     pages = {37-61},
     zbl = {0923.47006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv79z1p37bwm}
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Zieliński, Lech. Charge transfer scatteringin a constant electric field. Colloquium Mathematicae, Tome 79 (1999) pp. 37-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv79z1p37bwm/

[000] [1] T. Adachi and H. Tamura, Asymptotic completeness for long range many-particle systems with Stark effect, J. Math. Sci. Univ. Tokyo 2 (1995), 77-116. | Zbl 0843.35086

[001] [2] T. Adachi and H. Tamura, Asymptotic completeness for long range many-particle systems with Stark effect. II, Comm. Math. Phys. 174 (1996), 537-559. | Zbl 0849.35112

[002] [3] W. O. Amrein, A. Boutet de Monvel and V. Georgescu, Lp-inequalities for the Laplacian and unique continuation, Ann. Inst. Fourier (Grenoble) 31 (1981), no. 3, 153-168.

[003] [4] W. O. Amrein, A. Boutet de Monvel and V. Georgescu, C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Birkhäuser, 1996. | Zbl 0962.47500

[004] [5] J. E. Avron and I. W. Herbst, Spectral and scattering theory for Schrödinger operators related to Stark effect, Comm. Math. Phys. 52 (1977), 239-254. | Zbl 0351.47007

[005] [6] J. Dereziński and C. Gérard, Asymptotic Completeness of N-Particle Systems, Springer, 1996.

[006] [7] G. M. Graf, Phase space analysis of the charge transfer model, Helv. Phys. Acta 63 (1990), 107-138. | Zbl 0741.35050

[007] [8] G. M. Graf, Asymptotic completeness for N-body short-range quantum systems: a new proof, Comm. Math. Phys. 123 (1990), 107-138.

[008] [9] G. M. Graf, A remark on long-range Stark scattering, Helv. Phys. Acta 64 (1991), 1167-1174.

[009] [10] G. A. Hagedorn, Asymptotic completeness for the impact parameter approximation to the three particle scattering, Ann. Inst. H. Poincaré, Sect. A 36 (1982), 19-40. | Zbl 0482.47003

[010] [11] B. Helffer et J. Sjöstrand, Equation de Schrödinger avec champ magnétique et équation de Harper, in: Lecture Notes in Phys. 345, Springer, 1989, 118-197. | Zbl 0699.35189

[011] [12] I. W. Herbst, Unitary equivalence of Stark effect Hamiltonians, Math. Z. 155 (1977), 55-70. | Zbl 0338.47009

[012] [13] I. W. Herbst, J. S. Mοller and E. Skibsted, Spectral analysis of N-body Stark Hamiltonians, Comm. Math. Phys. 174 (1995), 261-294. | Zbl 0846.35095

[013] [14] I. W. Herbst, J. S. Mοller and E. Skibsted, Asymptotic completeness for N-body Stark Hamiltonians, ibid. 174 (1996), 509-535. | Zbl 0846.35096

[014] [15] A. Jensen, Scattering theory for Stark Hamiltonians, Proc. Indian Acad. Sci. (Math. Sci.) 104 (1994), 599-651. | Zbl 0827.47006

[015] [16] A. Jensen and T. Ozawa, Existence and non-existence results for wave operators for perturbations of the Laplacian, Rev. Math. Phys. 5 (1993), 601-629. | Zbl 0831.35145

[016] [17] A. Jensen and K. Yajima, On the long range scattering for Stark Hamiltonians, J. Reine Angew. Math. 420 (1991), 179-193. | Zbl 0736.35077

[017] [18] E. L. Korotyaev, On the scattering theory of several particles in an external electric field, Math. USSR-Sb. 60 (1988), 177-196.

[018] [19] P. A. Perry, Scattering Theory by the Enss Method, Math. Rep. 1, Harwood, 1983, 1-347. | Zbl 0529.35004

[019] [20] I. M. Sigal, Stark effect in multielectron systems: non-existence of bound states, Comm. Math. Phys. 122 (1989), 1-22. | Zbl 0684.35079

[020] [21] I. M. Sigal and A. Soffer, The N-particle scattering problem: asymptotic completeness for the short-range quantum systems, Ann. of Math. 125 (1987), 35-108.

[021] [22] H. Tamura, Scattering theory for N-particle systems with Stark effect: asymptotic completeness, RIMS Kyoto Univ. 29 (1993), 869-884. | Zbl 0831.35124

[022] [23] D. A. White, The Stark effect and long-range scattering in two Hilbert spaces, Indiana Univ. Math. J. 39 (1990), 517-546. | Zbl 0695.35144

[023] [24] D. A. White, Modified wave operators and Stark Hamiltonians, Duke Math. J. 68 (1992), 83-100. | Zbl 0766.35033

[024] [25] U. Wüller, Geometric methods in scattering theory of the charge transfer model, ibid. 62 (1991), 273-313. | Zbl 0732.35055

[025] [26] K. Yajima, A multi-channel scattering theory for some time dependent hamiltonians, Charge Transfer Problem, Comm. Math. Phys. 75 (1980), 153-178. | Zbl 0437.47008

[026] [27] K. Yajima, Spectral and scattering theory for Schrödinger operators with Stark effect, J. Fac. Sci. Univ. Tokyo Sect. IA 26 (1979), 377-390. | Zbl 0429.35027

[027] [28] K. Yajima, Spectral and scattering theory for Schrödinger operators with Stark effect, II, ibid. 28 (1981), 1-15.

[028] [29] L. Zieliński, Complétude asymptotique pour un modèle du transfert de charge, Ann. Inst. H. Poincaré Phys. Théor. 58 (1993), 363-411.

[029] [30] L. Zieliński, Scattering for a dispersive charge transfer model, ibid. 65 (1997), 339-386. | Zbl 0887.35110

[030] [31] L. Zieliński, Asymptotic completeness for multiparticle dispersive charge transfer model, J. Funct. Anal. 150 (1997), 453-470. | Zbl 0891.35134

[031] [32] L. Zieliński, Dispersive charge transfer model with long range interactions, J. Math. Anal. Appl. 217 (1998), 43-71. | Zbl 0913.35112

[032] [33] J. Zorbas, Scattering theory for Stark Hamiltonians involving long range potentials, J. Math. Phys. 19 (1978), 577-580.