Application of the statistical mechanics transformation theory to a soluble model
作者:
R.W. Gibberd,
C. George,
期刊:
Transport Theory and Statistical Physics
(Taylor Available online 1972)
卷期:
Volume 2,
issue 2
页码: 109-116
ISSN:0041-1450
年代: 1972
DOI:10.1080/00411457208232531
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
One of us (C.G) has developed a transformation theory in nonequilibrium statistical mechanics that generalizes the usual transformation theory of quantum mechanics in the framework of the resolvent formalism of the Liouville-von Neumann operator extensively used by the Brussels school. Prigogine, George, and Henin have shown that the evolution of a dissipative system can be decomposed into separate subdynamics in orthogonal subspaces. The π subspace, containing all thermodynamics, can be seen as an extension of the subspace of the invariants in the absence of dissipation. In this subspace a suitable contracted description of the system can be given through a dressing operator χ, which has the property that HR= χ−1H0can be considered as the renormalized energy. A differential equation that determines χ has been proposed by Mandel. It is useful to see, even for a nondissipative system, what relation the transformation theory in the Liouville-von Neumann formalism has to the standard transformations used in quantum mechanics. In this paper we consider a system that can be completely diagonalized by the Bogoliubov transformation. It is shown that in this case the Mandel equation can be solved and that χ−1H0= HD, where HDis the diagonalized Hamiltonian, obtained by the Bogoliubov transformation.
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