由多个二值噪声驱动的Ornstein-Uhlenbeck过程
Ornstein-Uhlenbeck Process Driven by Multiple Dichotomous Noises
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中文总结 AI 辅助
该研究分析由多个二值噪声驱动的广义Ornstein-Uhlenbeck过程，推导其平稳分布等精确表达式，建立与异质随机飞行过程的映射，揭示无序对平稳态的影响及多噪声源下的统计过渡特性。
中文摘要 AI 辅助
我们研究由K个独立二值噪声叠加驱动的广义Ornstein-Uhlenbeck过程，这些噪声具有任意固定的振幅和切换率。与由平衡高斯白噪声驱动的经典Ornstein-Uhlenbeck过程不同，当前系统由具有有限关联时间的有界非平衡涨落支配。我们获得了平稳位置分布和所有累积量的精确表达式，表明平稳态具有出乎意料的丰富结构，包括紧支集、代数分支点奇点、边缘发散和多个极值。我们建立了与具有有界跳跃的异质随机飞行过程的映射，为平稳测度提供了清晰的概率解释。我们进一步分析了几种极限 regime，包括大量噪声源下向高斯统计的过渡。对于具有指数分布淬火振幅的系综，我们推导了精确的无序平均平稳分布，表明无序从根本上改变了平稳态，产生了带有非平凡指数的代数 prefactor 修饰的指数尾。
英文摘要
We study a generalized Ornstein-Uhlenbeck process driven by a superposition of $K$ independent dichotomous noises with arbitrary fixed amplitudes and switching rates. Unlike the classical Ornstein-Uhlenbeck process driven by equilibrium Gaussian white noise, the present system is governed by bounded nonequilibrium fluctuations with finite correlation times. We obtain exact expressions for the stationary position distribution and all cumulants, and show that the stationary state possesses an unexpectedly rich structure, including compact support, algebraic branch-point singularities, edge divergences, and multiple extrema. We establish a mapping onto a heterogeneous random-flight process with bounded jumps, yielding a transparent probabilistic interpretation of the stationary measure. We further analyze several limiting regimes, including the crossover to Gaussian statistics for large numbers of noise sources. For ensembles with exponentially-distributed quenched amplitudes, we derive exact disorder-averaged stationary distributions and show that disorder fundamentally alters the stationary state, producing exponential tails decorated by algebraic prefactors with non-trivial exponents.
发表机构
- Sorbonne Université（索邦大学）
- CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600)（法国国家科学研究中心，凝聚态物质理论物理实验室）
- Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）
- Nanotech-CNR, UOS di Roma and INFN, Sezione di Roma（纳米技术-意大利国家研究委员会罗马单元及罗马分部INFN）
- Department of Physics, Pohang University of Science and Technology (POSTECH)（浦项科技大学物理系）
- Asia Pacific Center for Theoretical Physics (APCTP)（亚太理论物理中心）
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