Dynamics of Correlations of Bose and Fermi Particles
arXiv:1001.3893 · doi:10.1002/mma.1336
Abstract
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.
arXiv comment30 pages
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- Quantum Kinetic Equations of Many-Particle Systems in Condensed States
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- On Kinetic Equations for Collisional Dynamics of Active Soft Condensed Matter
- Mean Field Asymptotics of Generalized Quantum Kinetic Equation
- Introduction to the Theory of Evolution Equations of Quantum Many-Particle Systems
- On Operators Generated by Density Matrix
- On Dynamics of Correlations in Quantum Many-Particle Systems
- Cumulant expansions of operator groups of quantum many-particle systems
- Dynamics of correlations in a system of hard spheres