论文标题
挤压随机化学反应系统的固定分布
Squeezing stationary distributions of stochastic chemical reaction systems
论文作者
论文摘要
基于主方程的化学反应系统的随机建模一直是物理科学中必不可少的工具。在长期的限制中，这些系统的性质的特征是化学主方程的固定分布。在本文中，我们根据随机化学反应系统和第二个量化之间的平行形式形式来描述一种用于分析固定分布的新方法。 Anderson，Craciun和Kurtz表明，当反应网络的速率方程接收一个复杂平衡的稳态溶液时，相应的随机反应系统具有托有泊松分布的乘积形式的固定分布。在使用DOI启动的第二个量化语言的随机反应系统的制定中，产品形式的泊松分布对应于连贯的状态。进一步追求这种类比，我们研究了随机反应系统中挤压状态的对应物。在挤压操作员的作用下，化学主方程的时间进化操作员被转换，结果系统描述了不同的反应网络，该网络不接受复杂的平衡稳态。挤压的相干状态给出了转化网络的固定分布，为此获得了分析表达。
Stochastic modeling of chemical reaction systems based on master equations has been an indispensable tool in physical sciences. In the long-time limit, the properties of these systems are characterized by stationary distributions of chemical master equations. In this paper, we describe a novel method for computing stationary distributions analytically, based on a parallel formalism between stochastic chemical reaction systems and second quantization. Anderson, Craciun, and Kurtz showed that, when the rate equation for a reaction network admits a complex-balanced steady-state solution, the corresponding stochastic reaction system has a stationary distribution of a product form of Poisson distributions. In a formulation of stochastic reaction systems using the language of second quantization initiated by Doi, product-form Poisson distributions correspond to coherent states. Pursuing this analogy further, we study the counterpart of squeezed states in stochastic reaction systems. Under the action of a squeeze operator, the time-evolution operator of the chemical master equation is transformed, and the resulting system describes a different reaction network, which does not admit a complex-balanced steady state. A squeezed coherent state gives the stationary distribution of the transformed network, for which analytic expression is obtained.
