Doi-Peliti path integral methods for stochastic systems with partial exclusion

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Abstract

Doi-Peliti methods are developed for stochastic models with finite maximum occupation numbers per site. We provide a generalized framework for the different Fock spaces reported in the literature. Paragrassmannian techniques are then utilized to construct path integral formulations of factorial moments. We show that for many models of interest, a Magnus expansion is required to construct a suitable action, meaning actions containing a finite number of terms are not always feasible. However, for such systems, perturbative techniques are still viable, and for some examples, including carrying capacity population dynamics, and diffusion with partial exclusion, the expansions are exactly summable.
Original languageEnglish
Pages (from-to)211-221
Number of pages11
JournalPhysica A: Statistical Mechanics and Its Applications
Volume505
Early online date29 Mar 2018
DOIs
Publication statusPublished - 1 Sep 2018

Keywords

  • Doi-peliti
  • Path integral
  • Partial exclusion
  • Carrying capacity
  • Population dynamics

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