Asymptotic completeness for a quantum particle in a Markovian short range potential. (English) Zbl 0618.60086
Author’s abstract: Absence of bound states and asymptotic completeness are proven for a quantum particle in a time dependent random (Markovian) short range potential. Systems with confining potentials are also considered and unboundedness of the energy in time is shown.
Reviewer: U.F.Wodarzik
References:
| [1] | Pillet, C. A.: Some results on the quantum dynamics of a particle in a Markovian potential. Commun. Math. Phys.102, 237-254 (1985) · Zbl 0591.60073 · doi:10.1007/BF01229379 |
| [2] | Enss, V.: In: Rigorous atomic and molecular physics. Velo G., Wightman, A. S. (eds.), New York: Plenum Press 1980/81 |
| [3] | Ginibre, J.: La méthode ?dépendent du temps? dans le problème de la complétude asymptotique, exposé présenté à l’Institut de Recherches Mathématiques Avancées de l’Université de Strasbourg, Mai 79, preprint 1980 |
| [4] | Jafaev, D. R.: preprint Leningrad Branch Mathematical Institute E-2-79, 1979 |
| [5] | Jafaev, D. R.: Sov. Math. Dokl.21, 545-549 (1980) |
| [6] | Kato, T.: J. Fac. Sci. Univ. Tokyo, Sect. I A Math.17, 241-258 (1970) |
| [7] | Simon, B.: Functional integration and quantum physics. New York: Academic Press 1979 · Zbl 0434.28013 |
| [8] | Reed, M., Simon, B.: Scattering theory. New York: Academic Press 1979 · Zbl 0405.47007 |
| [9] | Reed, M., Simon, B.: Fourier analysis, self adjointness. New York: Academic Press 1975 · Zbl 0308.47002 |
| [10] | Titchmarsh, E. C.: The theory of functions. London: Oxford University Press 1959 · Zbl 0092.10503 |
| [11] | Simon, B.: Trace ideal methods. New York: Cambridge University Press 1979 |
| [12] | Bergh, J., Löfström, J.: Interpolation spaces. Berlin, Heidelberg, New York: Springer 1976 · Zbl 0344.46071 |
| [13] | Reed, M., Simon, B.: Analysis of operators. New York: Academic Press 1978 · Zbl 0401.47001 |
| [14] | Yajima, K.: A multi-channel scattering theory for some time-dependent Hamiltonians, charge transfer problem. Commun. Math. Phys.75, 153-178 (1980) · Zbl 0437.47008 · doi:10.1007/BF01222515 |
| [15] | Reed, M., Simon, B.: Functional analysis. New York: Academic Press 1980 · Zbl 0459.46001 |
| [16] | Lions, J. L., Magenes, E.: Non-homogeneous boundary value problems and applications I. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0223.35039 |
| [17] | Hagedorn, G., Loss, M., Slawny, J.: to appear in J. Phys. A |
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