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Coherent spin states and stochastic hybrid path integrals
Journal of Statistical Mechanics: Theory and Experiment ( IF 2.4 ) Pub Date : 2021-04-16 , DOI: 10.1088/1742-5468/abf1e9
Paul C Bressloff

Stochastic hybrid systems involve a coupling between a discrete Markov chain and a continuous stochastic process. If the latter evolves deterministically between jumps in the discrete state, then the system reduces to a piecewise deterministic Markov process. Well known examples include stochastic gene expression, voltage fluctuations in neurons, and motor-driven intracellular transport. In this paper we use coherent spin states to construct a new path integral representation of the probability density functional for stochastic hybrid systems, which holds outside the weak noise regime. We use the path integral to derive a system of Langevin equations in the semi-classical limit, which extends previous diffusion approximations based on a quasi-steady-state reduction. We then show how in the weak noise limit the path integral is equivalent to an alternative representation that was previously derived using Doi–Peliti operators. The action functional of the latter is related to a large deviation principle for stochastic hybrid systems.



中文翻译:

相干自旋态和随机混合路径积分

随机混合系统涉及离散马尔可夫链和连续随机过程之间的耦合。如果后者在离散状态的跳跃之间确定性地演化,则系统简化为分段确定性马尔可夫过程。众所周知的例子包括随机基因表达、神经元电压波动和电机驱动的细胞内运输。在本文中,我们使用相干自旋状态来构建随机混合系统的概率密度泛函的新路径积分表示,它在弱噪声范围之外成立。我们使用路径积分推导出半经典极限中的朗之万方程组,它扩展了先前基于准稳态减少的扩散近似。然后,我们展示了在弱噪声限制下,路径积分如何等效于先前使用 Doi-Peliti 算子导出的替代表示。后者的作用泛函与随机混合系统的大偏差原理有关。

更新日期:2021-04-16
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