zbMATH — the first resource for mathematics

Bogoliubov type equations via infinite-dimensional equations for measures. (English) Zbl 1246.82007
Accardi, Luigi (ed.) et al., Quantum bio-informatics IV. From quantum information to bio-informatics, Tokyo, Japan, March 10–13, 2010. Selected papers based on the presentations at the international conference. Hackensack, NJ: World Scientific (ISBN 978-981-4343-75-6/hbk; 978-981-4343-76-3/ebook). QP-PQ: Quantum Probability and White Noise Analysis 28, 321-337 (2011).
As an introduction, the classical case is considered, when the state is described by a nonnegative measure on the phase space. Then, the Wigner measure is defined, and its properties and evolution equation are reviewed. Based on the similarity of the Liouville equation and that one based on the Wigner measure, quantum analogues are formulated, and their classical relationship is studied. A Poincaré model is then discussed for the irreversible case, and the observation is made that it is symmetrical with respect to time evolution.
For the entire collection see [Zbl 1234.81012].
82B05 Classical equilibrium statistical mechanics (general)
82B30 Statistical thermodynamics
81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
82B10 Quantum equilibrium statistical mechanics (general)
Full Text: Link