Abstract
The existence of a unique solution, in terms of initial data of the BBGKY hierarchy of quantum kinetic equations with coulomb potential, is proved. This is based on non-relativistic quantum mechanics and utilizing a semigroup method.
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N. N. Bogolyubov, Problems of a Dynamical Theory in Statistical Physics (Gostehizdat, Moscow, 1946); N.N. Bogolyubov, Lectures on Quantum Statistics (Radyanska Shkola, Kiev, 1949).
N. N. Bogolyubov and N. N. Bogolyubov, Jr., Introduction to Quantum Statistical Mechanics (Nauka, Moscow, 1984).
E. H. Lieb and J. L. Lebowitz, Springer Lecture Notes Phys. 20, 136 (1973).
T. Kato, Perturbation Theory for Linear Operators (Springer, Berlin, Heidelberg, New York, 1966).
D. Ya. Petrina and A. K. Vidibida, Trudi MI ANUSSR 136, 370 (1975).
D. Ya. Petrina, Mathematical Foundation of Quantum Statistical Mechanics, Continuous Systems (Kluwer Acad., Dordrecht, Boston, London, 1995).
M. Yu. Rasulova, Dokl. Akad. Nauk UzSSR 2, 248 (1976).
I. Gohberg, S. Goldberg, and M. A. Kaashoek, Classes of Linear Operators, Vol. 1 (Birkhäuser, Basel, Boston, Berlin, 1990).
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations (Springer, New York, Berlin, Heidelberg, London, Paris, Tokyo, Hong Kong, Barcelona, Budapest, 1983).
M. Reed and B. Saymon, Methods of Modern Mathematical Physics, Vol. 2 (Academic, New York, San Francisco, London, 1975).
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Talk at the International Bogolyubov Conference Problems of Theoretical and Mathematical Physics, Moscow-Dubna, Russia August 21–27, 2009.
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Brokate, M., Rasulova, M.Y. The cauchy problem for BBGKY hierarchy of quantum kinetic equations with coulomb potential. Phys. Part. Nuclei 41, 1014–1016 (2010). https://doi.org/10.1134/S1063779610070063
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DOI: https://doi.org/10.1134/S1063779610070063