Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$

M. V. Platonova; S. V. Tsykin

Geodesic

Parcourir par

Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$

M. V. Platonova ; S. V. Tsykin

Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 78-81

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

Résumé

Two approaches are suggested for constructing a probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$, in the strong operator topology. In the first approach, the approximating operators have the form of expectations of functionals of a certain Poisson point field, while, in the second approach, the approximating operators have the form of expectations of functionals of sums of independent identically distributed random variables with finite moments of order $2m+2$.

Keywords: Schrödinger equation, Poisson random measures, limit theorems.

@article{DANMA_2020_491_a15,
     author = {M. V. Platonova and S. V. Tsykin},
     title = {Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {78--81},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_491_a15/}
}

TY  - JOUR
AU  - M. V. Platonova
AU  - S. V. Tsykin
TI  - Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 78
EP  - 81
VL  - 491
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_491_a15/
LA  - ru
ID  - DANMA_2020_491_a15
ER  -

%0 Journal Article
%A M. V. Platonova
%A S. V. Tsykin
%T Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 78-81
%V 491
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2020_491_a15/
%G ru
%F DANMA_2020_491_a15

M. V. Platonova; S. V. Tsykin. Probabilistic approximation of the evolution operator $e^{itH}$, where $H=\dfrac{(-1)^md^{2m}}{(2m)!dx^{2m}}$. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 491 (2020), pp. 78-81. http://geodesic.mathdoc.fr/item/DANMA_2020_491_a15/