Advances in Theoretical and Mathematical Physics

Volume 26 (2022)

Number 9

Chemical kinetics, Markov chains, and the imaginary Itô interpretation

Pages: 3017 – 3068

DOI: https://dx.doi.org/10.4310/ATMP.2022.v26.n9.a4

Authors

Álvaro Correales (Departamento de Matemáticas, Universidad Autónoma de Madrid, Spain)

Carlos Escudero (Departamento de Matemáticas Fundamentales, Universidad Nacional de Educación a Distancia, Madrid, Spain)

Mariya Ptashnyk (Department of Mathematics, Heriot-Watt University, Edinburgh United Kingdom)

Abstract

The abstract chemical reaction\[A + A \to \emptyset \quad \textrm{,}\]understood as a Markov chain in continuous time, has been studied in the physical literature for several years. It has been claimed that this reaction can be described by means of the stochastic differential equation\[d \phi = -\phi^2 dt + i \, \phi \, dW_t \quad \textrm{,}\]where $i$ is the imaginary unit. This affirmation is, at least, intriguing, and has led to controversy and criticisms in the literature. The goal of this work is to give partial evidence that such a description may be possible.

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Published 30 October 2023