论文标题
随机动力学系统的最可能的动力学，带有指数的轻跳波动
Most Probable Dynamics of Stochastic Dynamical Systems with Exponentially Light Jump Fluctuations
论文作者
论文摘要
从有限域中出现的出现，该域中包含由非高斯lévy波动引起的稳定固定点的出现，在实际物理系统中起着关键作用。在噪声较弱的极限下，我们在莱维（Lévy）波动下发展了一种哈密顿形式主义，其一维随机动力学系统的呈指数跳跃。这种形式主义基于在非高斯lévy扰动下用于动态系统的最近证明的大偏差原理。我们演示了如何通过几个示例来计算最可能的出口路径和准电位。同时，我们探讨了跳跃措施对准势定量和最可能的出口路径的影响。结果表明，准潜电可以通过近似分析表达来很好地估计。此外，我们发现，尽管最可能的出口路径类似于与高斯的各向同性噪声相似，但各向异性噪声导致出口路径结构的显着变化。这些发现阐明了非高斯噪声引起的退出现象的基本定性机制和定量特征。
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian Lévy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian formalism under the Lévy fluctuations with exponentially light jumps for one- and two-dimensional stochastic dynamical systems. This formalism is based on a recently proved large deviation principle for dynamical systems under non-Gaussian Lévy perturbations. We demonstrate how to compute the most probable exit path and the quasi-potential by several examples. Meanwhile, we explore the impacts of the jump measure on the quasi-potential quantitatively and on the most probable exit path qualitatively. Results show that the quasi-potential can be well estimated by an approximate analytical expression. Moreover, we discover that although the most probable exit paths are analogous to the Gaussian case for the isotropic noise, the anisotropic noise leads to significant changes of the structure of the exit paths. These findings shed light on the underlying qualitative mechanism and quantitative feature of the exit phenomenon induced by non-Gaussian noise.
