On quantum dynamics on $C^*$-algebras
Informatics and Automation, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 33-47
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We consider the problem of constructing quantum dynamics for symmetric Hamiltonian operators that have no self-adjoint extensions. For an earlier studied model, it was found that an elliptic self-adjoint regularization of a symmetric Hamiltonian operator allows one to construct quantum dynamics for vector states on certain $C^*$-subalgebras of the algebra of bounded operators in a Hilbert space. In the present study, we prove that one can extend the dynamics to arbitrary states on these $C^*$-subalgebras while preserving the continuity and convexity. We show that the obtained extension of the dynamics of the set of states on $C^*$-subalgebras is the limit of a sequence of regularized dynamics under removal of the elliptic regularization. We also analyze the properties of the limit dynamics of the set of states on the $C^*$-subalgebras.
@article{TRSPY_2018_301_a2,
author = {I. V. Volovich and V. Zh. Sakbaev},
title = {On quantum dynamics on $C^*$-algebras},
journal = {Informatics and Automation},
pages = {33--47},
publisher = {mathdoc},
volume = {301},
year = {2018},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2018_301_a2/}
}
I. V. Volovich; V. Zh. Sakbaev. On quantum dynamics on $C^*$-algebras. Informatics and Automation, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 33-47. http://geodesic.mathdoc.fr/item/TRSPY_2018_301_a2/