5 research outputs found
Hydrodynamic Equations for Microscopic Phase Densities
The evolution equations for the generalized microscopic phase densities are
introduced. The evolution equations of average values of microscopic phase
densities are derived and a solution of the initial-value problem of the
obtained hydrodynamic type hierarchy is constructed.Comment: 4 page
On the solutions of the nonlinear Liouville hierarchy
We investigate the initial-value problem of the non-linear Liouville
hierarchy. For the general form of the interaction potential we construct an
explicit solution in terms of an expansion over particle clusters whose
evolution is described by the corresponding-order cumulant of evolution
operators of a system of finitely many particles. For the initial data from the
space of integrable functions the existence of a strong solution of the Cauchy
problem is proved.Comment: 9 page
The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems
The Cauchy problem for the von Neumann hierarchy of nonlinear equations is
investigated. One describes the evolution of all possible states of quantum
many-particle systems by the correlation operators. A solution of such
nonlinear equations is constructed in the form of an expansion over particle
clusters whose evolution is described by the corresponding order cumulant
(semi-invariant) of evolution operators for the von Neumann equations. For the
initial data from the space of sequences of trace class operators the existence
of a strong and a weak solution of the Cauchy problem is proved. We discuss the
relationships of this solution both with the -particle statistical
operators, which are solutions of the BBGKY hierarchy, and with the
-particle correlation operators of quantum systems.Comment: 26 page