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

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  • Greenman, Chris D.

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.

Suggested Citation

  • Greenman, Chris D., 2018. "Doi–Peliti path integral methods for stochastic systems with partial exclusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 211-221.
    • Handle: RePEc:eee:phsmap:v:505:y:2018:i:c:p:211-221
    DOI: 10.1016/j.physa.2018.03.045
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    References listed on IDEAS

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    1. Silva, Érica M. & Muzy, Paulo T. & Santana, Ademir E., 2008. "Fock space for fermion-like lattices and the linear Glauber model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5101-5109.
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