Geodesic
Random quantization of Hamiltonian systems
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 31-36

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

A quantization of a Hamiltonian system is an ambiguous procedure. Accordingly, we introduce the notion of random quantization, related random variables with values in the set of self-adjoint operators, and random processes with values in the group of unitary operators. The procedures for the averaging of random unitary groups and averaging of random self-adjoint operators are defined. The generalized weak convergence of a sequence of measures and the corresponding generalized convergence in distribution of a sequence of random variables are introduced. The generalized convergence in distribution for some sequences of compositions of random mappings is obtained. In the case of a sequence of compositions of shifts by independent random vectors of Euclidean space, the obtained convergence coincides with the statement of the central limit theorem for a sum of independent random vectors. The results are applied to the dynamics of quantum systems arising in random quantization of a Hamiltonian system.
Keywords: random linear operator, random operator-valued function, operator-valued random process, law of large numbers, central limit theorem, Markovian process, Kolmogorov equation. 
@article{DANMA_2021_498_a5,
     author = {J. E. Gough and Yu. N. Orlov and V. Zh. Sakbaev and O. G. Smolyanov},
     title = {Random quantization of {Hamiltonian} systems},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {31--36},
     publisher = {mathdoc},
     volume = {498},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_498_a5/}
}
TY  - JOUR
AU  - J. E. Gough
AU  - Yu. N. Orlov
AU  - V. Zh. Sakbaev
AU  - O. G. Smolyanov
TI  - Random quantization of Hamiltonian systems
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 31
EP  - 36
VL  - 498
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2021_498_a5/
LA  - ru
ID  - DANMA_2021_498_a5
ER  - 
%0 Journal Article
%A J. E. Gough
%A Yu. N. Orlov
%A V. Zh. Sakbaev
%A O. G. Smolyanov
%T Random quantization of Hamiltonian systems
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2021
%P 31-36
%V 498
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2021_498_a5/
%G ru
%F DANMA_2021_498_a5
J. E. Gough; Yu. N. Orlov; V. Zh. Sakbaev; O. G. Smolyanov. Random quantization of Hamiltonian systems. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 498 (2021), pp. 31-36. http://geodesic.mathdoc.fr/item/DANMA_2021_498_a5/