Dynamics of correlations of Bose and Fermi particles

作者：Gerasimenko V I; Polishchuk D O^*

来源：Mathematical Methods in the Applied Sciences, 2011, 34(1): 76-93.

DOI：10.1002/mma.1336

• von Neumann hierarchy
• Fermi-Dirac and Bose-Einstein statistics
• correlation operator
• density matrix
• marginal operators
• quantum many-particle system

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, in particular for initial data satisfying a chaos property.

• 出版日期2011-1-15