arXiv:0804.1153 · Birkhäuser Basel eBooks

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

V. I. Gerasimenko

Published Jan 1, 2009• 5 citations

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.

DOI: 10.1007/978-3-7643-9921-4_21

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