On the Initial-Value Problem to the Quantum Dual BBGKY Hierarchy
Mathematical Physics
2011-01-21 v1 Statistical Mechanics
Dynamical Systems
math.MP
Abstract
We develop a rigorous formalism for the description of the evolution of observables in quantum systems of particles. We construct a solution of the initial-value problem to the quantum dual BBGKY hierarchy of equations as an expansion over particle clusters whose evolution are governed by the corresponding-order dual cumulant (dual semi-invariant) of the evolution operators of finitely many particles. For initial data from the space of sequences of bounded operators the existence and uniqueness theorem is proved.
Cite
@article{arxiv.0806.1027,
title = {On the Initial-Value Problem to the Quantum Dual BBGKY Hierarchy},
author = {G. Borgioli and V. Gerasimenko},
journal= {arXiv preprint arXiv:0806.1027},
year = {2011}
}
Comments
22 pages