Operator Approach to the Master Equation for the One-Step Process
1 Department of Applied Probability and Informatics, Peoples’ Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow, 117198, Russia
2 Laboratory of Information Technologies, Joint Institute for Nuclear Research, Joliot-Curie 6, Dubna, Moscow region, 141980, Russia
3 Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Joliot-Curie 6, Dubna, Moscow region, 141980, Russia
4 Department of Theoretical Physics, SAS, Institute of Experimental Physics, Watsonova 47, 040 01 Košice, Slovakia
5 Faculty of Science, P. J. Šafárik University, Šrobárova 2, 041 54 Košice, Slovakia
Published online: 9 February 2016
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, published by EDP Sciences, 2016
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