反应网络的量子技术
Quantum Techniques for Reaction Networks
摘要：
反应网络是描述经典实体以随机方式相互作用的一般形式。虽然反应网络主要由化学家研究，但它们相当于Petri网，在计算机科学和生物学中用于类似的目的。正如土井和其他人所指出的，来自量子场论的技术可以适用于这样的系统。在这里，我们使用这些技术来研究如何“主方程”描述的随机时间演化的反应网络是相关的“速率方程”描述的确定性演化的预期数量的每个物种的粒子在大数限制。我们发现，当主方程的解是一个“相干态”时，这种关系特别强，这意味着每种实体的数量由独立的泊松分布描述。
英文摘要：
Reaction networks are a general formalism for describing collections of classical entities interacting in a random way. While reaction networks are mainly studied by chemists, they are equivalent to Petri nets, which are used for similar purposes in computer science and biology. As noted by Doi and others, techniques from quantum field theory can be adapted to apply to such systems. Here we use these techniques to study how the "master equation" describing stochastic time evolution for a reaction network is related to the "rate equation" describing the deterministic evolution of the expected number of particles of each species in the large-number limit. We show that the relation is especially strong when a solution of master equation is a "coherent state", meaning that the numbers of entities of each kind are described by independent Poisson distributions.
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