# Two Langevin equations in the Doi-Peliti formalism

Source: [Two Langevin equations in the Doi-Peliti formalism](<https://www.sota2.com/research/paper/68fa29161e209131ce831041>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:53:00.160Z

Authors: Kazunori Itakura, Jun Ohkubo, Shin-ichi Sasa

Published: 2009-12-09T02:42:45.000Z

## Abstract

A system-size expansion method is incorporated into the Doi-Peliti formalism for stochastic chemical kinetics. The basic idea of the incorporation is to introduce a new decomposition of unity associated with a so-called Cole-Hopf transformation. This approach elucidates a relationship between two different Langevin equations; one is associated with a coherent-state path-integral expression and the other describes density fluctuations. A simple reaction scheme $X \\rightleftarrows X+X$ is investigated as an illustrative example.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0912.1652>)

[PDF](<https://arxiv.org/pdf/0912.1652.pdf>)