Geodesic
On quantum dynamics on $C^*$-algebras
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 33-47

Voir la notice de l'article provenant de la source Math-Net.Ru

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{TM_2018_301_a2,
     author = {I. V. Volovich and V. Zh. Sakbaev},
     title = {On quantum dynamics on $C^*$-algebras},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {33--47},
     publisher = {mathdoc},
     volume = {301},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_301_a2/}
}
TY  - JOUR
AU  - I. V. Volovich
AU  - V. Zh. Sakbaev
TI  - On quantum dynamics on $C^*$-algebras
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2018
SP  - 33
EP  - 47
VL  - 301
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2018_301_a2/
LA  - ru
ID  - TM_2018_301_a2
ER  - 
%0 Journal Article
%A I. V. Volovich
%A V. Zh. Sakbaev
%T On quantum dynamics on $C^*$-algebras
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2018
%P 33-47
%V 301
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2018_301_a2/
%G ru
%F TM_2018_301_a2
I. V. Volovich; V. Zh. Sakbaev. On quantum dynamics on $C^*$-algebras. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Complex analysis, mathematical physics, and applications, Tome 301 (2018), pp. 33-47. http://geodesic.mathdoc.fr/item/TM_2018_301_a2/