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An application of C-algebras to quantum statistical mechanics of systems in equilibrium

Marinus Winnink

Published Jan 1, 1968• 14 citations
OpenAlex

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The derivation of macroscopic irreversible dynamics of nonequilibrium systems from microscopic equations was recently revisited from the point of view of infinitely extended quantum systems. Here we have briefly reviewed the $C^*$ algebra and its application to equilibrium systems as well as introduced some recent results on NESS. In addition, we have demonstrated the derivation of Landauer formula rigorously for quadratic systems but using a more physical presentation.

arXiv:1110.6433•Oct 28, 2011•1 citation
The non-relativistic current algebra approach is analyzed subject to its application to studying the distribution functions of many-particle systems at the temperature equilibrium and their stability properties.We show that the classical Bogolubov generating functional method is a very effective tool for constructing the irreducible current algebra representations and the corresponding different generalized measure expansions including collective variables transform.The effective Hamiltonian operator construction and its spectrum peculiarities subject to the stability of equilibrium many-particle systems are discussed.
Quantum statistical mechanics in infinitely extended systems (C∗C^*C∗ algebraic approach)
The derivation of macroscopic irreversible dynamics of nonequilibrium systems from microscopic equations was recently revisited from the point of view of infinitely extended quantum systems. Here we have briefly reviewed the C∗C^*C∗ algebra and its application to equilibrium systems as well as introduced some recent results on NESS. In addition, we have demonstrated the derivation of Landauer formula rigorously for quadratic systems but using a more physical presentation.