Feynman averaging of semigroups generated by Schrödinger operators

The extension of averaging procedure for operator-valued function is defined by means of the integration of measurable map with respect to complex-valued measure or pseudomeasure. The averaging procedure of one-parametric semigroups of linear operators based on Chernoff equivalence for operator-valued functions is constructed. The initial value problem solutions are investigated for fractional diffusion equation and for Schrödinger equation with relativistic Hamiltonian of free motion. It is established that in these examples the solution of evolutionary equation can be obtained by applying the constructed averaging procedure to the random translation operators in classical coordinate space. © 2018 World Scientific Publishing Company.

Authors
Borisov L.A.1 , Orlov Y.N. 1, 2 , Sakbaev V.Z. 3
Journal
Infinite Dimensional Analysis, Quantum Probability and Related Topics
Publisher
World Scientific Publishing Co. Pte Ltd
Number of issue
2
Language
English
Status
Published
Link
External link
DOI
10.1142/S0219025718500108
Number
1850010
Volume
21
Year
2018
Organizations
  • 1 Keldysh Institute of Applied Mathematics Ras, Miusskaya sq., 4, Moscow, 125047, Russian Federation
  • 2 Peoples Friendship University of Russia, Miklukho-Maklay Street, 6, Moscow, 117198, Russian Federation
  • 3 Department of General Mathematics, Moscow Institute of Physics and Technology, Institutskiy per. 9, Dolgoprudny, Moscow Region, 141700, Russian Federation
Keywords
Chernoff equivalence; Chernoff theorem; Feynman formula; One-parametric semigroup; random variable
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6625/
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