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Usage de l'algebre de lie su( n ) dans l'etude des systems à n etats. VI. Equations linéaires d'evolution positive
Author(s) -
Van Groenendael A.
Publication year - 1986
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560300115
Subject(s) - evolution equation , lie algebra , mathematical physics , mathematics , yang–baxter equation , liouville equation , physics , quantum , pure mathematics , mathematical analysis , quantum mechanics
The n ‐level quantum system density‐operators evolution is not usually given by the Liouville equation, but by a more general one. This equation must keep density‐operators trace, hermiticity, and positiveness. These three conditions restrict the available kinds of evolution equations. In this paper we investigate linear equations for systems without memory effects. By using the first two conditions and the formalism we introduced in earlier papers, the evolution equation takes the form of a first order differential equation concerning the n 2 – 1 dimension “coherence‐vector.” The third one is the essential object of this paper. Moreover, we obtain a cononical splitting of this equation into four parts that may be separately studied.