We present a rigorous formalism to describe the evolution of observables of quantum many-particle systems. We construct a solution of the initial-value problem of the quantum dual BBGKY hierarchy of equations as an expansion over particle clusters, whose evolution is governed by the corresponding-order cumulant (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. PACS 05.30.-d – Quantum statistical mechanics. PACS 03.65.-w – Quantum mechanics. PACS 05.20.Dd – Kinetic theory.
Initial-value problem of the quantum dual BBGKY hierarchy / G.Borgioli;V.Gerasimenko. - In: NUOVO CIMENTO DELLA SOCIETÀ ITALIANA DI FISICA. C, GEOPHYSICS AND SPACE PHYSICS. - ISSN 1826-9885. - STAMPA. - 33C:(2010), pp. 71-78. [10.1393/ncc/i2010-10564-6]
Initial-value problem of the quantum dual BBGKY hierarchy
BORGIOLI, GIOVANNI;
2010
Abstract
We present a rigorous formalism to describe the evolution of observables of quantum many-particle systems. We construct a solution of the initial-value problem of the quantum dual BBGKY hierarchy of equations as an expansion over particle clusters, whose evolution is governed by the corresponding-order cumulant (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. PACS 05.30.-d – Quantum statistical mechanics. PACS 03.65.-w – Quantum mechanics. PACS 05.20.Dd – Kinetic theory.
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