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Groups of Operators for Evolution Equations of Quantum Many-particle Systems

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Modern Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 191))

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Abstract

The aim of this work is to study the properties of groups of operators for evolution equations of quantum many-particle systems, namely, the von Neumann hierarchy for correlation operators, the BBGKY hierarchy for marginal density operators and the dual BBGKY hierarchy for marginal observables. We show that the concept of cumulants (semi-invariants) of groups of operators for the von Neumann equations forms the basis of the expansions for one-parametric families of operators of various evolution equations for infinitely many particles.

This work was partially supported by the WTZ grant No M/124 (UA 04/2007) and by the project of NAS of Ukraine No 0107U002333.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, National Academy of Science of Ukraine, 3 Tereshchenkivs’ka St., 01601, Kyiv, Ukraine

    V. I. Gerasimenko

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  1. V. I. Gerasimenko
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Vadim M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Israel Gohberg

  3. Insitute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska st., 01601, Kyiv-4, Ukraine

    Anatoly Kochubei , Yurij Berezansky , Myroslav Gorbachuk  & Valentyna Gorbachuk , ,  & 

  4. Department of Mathematical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Gennadiy Popov

  5. Institute of Analysis and Scientific Computing, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Heinz Langer

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Gerasimenko, V.I. (2009). Groups of Operators for Evolution Equations of Quantum Many-particle Systems. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 191. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9921-4_21

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