Operator Approach to the Master Equation for the One-Step Process

Background. Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The kinetics of the interaction has recently attracted attention because it often occurs in the physical, chemical, technical, biological, environmental, economic, and sociological systems. However, there are no general methods for the direct study of this equation. The expansion of the equation in a formal Taylor series (the so called Kramers-Moyal's expansion) is used in the procedure of stochastization of one-step processes. Purpose. However, this does not eliminate the need for the study of the master equation. Method. It is proposed to use quantum field perturbation theory for the statistical systems (the so-called Doi method). Results. This work is a methodological material that describes the principles of master equation solution based on quantum field perturbation theory methods. The characteristic property of the work is that it is intelligible for non-specialists in quantum field theory. Conclusions. We show the full equivalence of the operator and combinatorial methods of obtaining and study of the one-step process master equation. © Owned by the authors.

Авторы
Hnatič M.3, 4, 5 , Eferina E.G. 1 , Korolkova A.V. 1 , Kulyabov D.S. 1, 2 , Sevastyanov L.A. 3, 1
Сборник материалов конференции
Издательство
EDP Sciences
Язык
Английский
Статус
Опубликовано
Номер
02027
Том
108
Год
2016
Организации
  • 1 Department of Applied Probability and Informatics, Peoples' Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
  • 2 Laboratory of Information Technologies, Joint Institute for Nuclear Research, Joliot-Curie 6, Dubna, Moscow region, 141980, Russian Federation
  • 3 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, 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, P. J. Šafárik University, Šrobárova 2, Košice, 041 54, Slovakia
Дата создания
19.10.2018
Дата изменения
01.03.2021
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/4009/
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