Geodesic
The set of quantum states and its averaged dynamic transformations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 48-58

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In this paper we consider the set of quantum states and passages to the limit for sequences of quantum dynamic semigroups in the mentioned set. We study the structure of the set of extreme points of the set of quantum states and represent an arbitrary state as an integral over the set of one-dimensional orthogonal projectors; the obtained representation is similar to the spectral decomposition of the normal state. We apply the obtained results to the analysis of the limit behavior of sequences of quantum dynamic semigroups which occur in the regularization of the degenerate Hamiltonian.
Keywords: finitely additive measure, quantum state, dynamic semigroup. 
@article{IVM_2011_10_a5,
     author = {V. Z. Sakbaev},
     title = {The set of quantum states and its averaged dynamic transformations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {48--58},
     publisher = {mathdoc},
     number = {10},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_10_a5/}
}
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V. Z. Sakbaev. The set of quantum states and its averaged dynamic transformations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2011), pp. 48-58. http://geodesic.mathdoc.fr/item/IVM_2011_10_a5/