Diagram representation for the stochastization of single-step processes

Background. By the means of the method of stochastization of one-step processes we get the simplified mathematical model of the original stochastic system. We can explore these models by standard methods, as opposed to the original system. The process of stochastization depends on the type of the system under study. Purpose. We want to get a unified abstract formalism for stochastization of one-step processes. This formalism should be equivalent to the previously introduced. Methods. To unify the methods of construction of the master equation, we propose to use the diagram technique. Results. We get a diagram technique, which allows to unify getting master equation for the system under study. We demonstrate the equivalence of the occupation number representation and the state vectors representation by using a Verhulst model. Conclusions. We have suggested a convenient diagram formalism for unified construction of stochastic systems. © Springer International Publishing AG 2016.

Авторы
Eferina E.G. 1 , Hnatich M.3, 4, 5 , Korolkova A.V. 1 , Kulyabov D.S. 1, 2 , Sevastianov L.A. 1, 3 , Velieva T.R. 1
Издательство
Springer Verlag
Язык
Английский
Страницы
483-497
Статус
Опубликовано
Том
678
Год
2016
Организации
  • 1 Department of Applied Probability and Informatics, RUDN University (Peoples’ Friendship University of Russia), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
  • 2 Laboratory of Information Technologies, Joint Institute for Nuclear Research, 6 Joliot-Curie, Dubna, Moscow Region 141980, Russian Federation
  • 3 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 6 Joliot-Curie, Dubna, Moscow Region 141980, Russian Federation
  • 4 Department of Theoretical Physics, SAS, Institute of Experimental Physics, Watsonova 47, Košice, 040 01, Slovakia
  • 5 Faculty of Science, Pavol Jozef Šafárik University in Košice (UPJŠ), Šrobárova 2, Košice, 041 80, Slovakia
Ключевые слова
Diagram technique; Diracnotation; Fock space; Master equation; Occupation numbers representation; One-step processes
Дата создания
19.10.2018
Дата изменения
01.03.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/4441/