部分排除随机系统的Doi-Peliti路径积分方法
Doi-Peliti Path Integral Methods for Stochastic Systems with Partial Exclusion
摘要：
Doi-Peliti方法被开发用于每个站点具有有限最大占用数的随机模型。我们提供了一个广义的框架不同的Fock空间在文献中报道。Paragrassmannian技术，然后利用构造路径积分配方的阶乘时刻。我们表明，对于许多感兴趣的模型，需要一个马格纳斯展开来构造一个合适的动作，这意味着包含有限数量的条款的行动并不总是可行的。然而，对于这样的系统，微扰技术仍然是可行的，并且对于一些例子，包括承载能力种群动力学和部分排斥扩散，扩展是完全可求和的。
英文摘要：
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.
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