Dynamics of Correlations of Bose and Fermi Particles

Details Dynamics of Correlations of Bose and Fermi Particles Dynamics of Correlations of Bose and Fermi Particles

2010-01-21

arxiv.org/abs/1001.3893v1

Math. Meth. Appl. Sci. 34 (1) (2011) 76-93

Physics

Mathematical Physics

30 pages

Scientific paper

10.1002/mma.1336

We discuss the origin of the microscopic description of correlations in quantum many-particle systems obeying Fermi-Dirac and Bose-Einstein statistics. For correlation operators that give the alternative description of the quantum state evolution of Bose and Fermi particles, we deduce the von Neumann hierarchy of nonlinear equations and construct the solution of its initial-value problem in the corresponding spaces of sequences of trace class operators. The links of constructed solution both with the solution of the quantum BBGKY hierarchy and with the nonlinear BBGKY hierarchy for marginal correlation operators are discussed. The solutions of the Cauchy problems of these hierarchies are constructed for initial data satisfying a chaos property.

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