异质Cattaneo-Vernotte方程与噪声投票模型的联系
Heterogeneous Cattaneo-Vernotte equation connection to the noisy voter model
AI总结：
研究通过连续方程和本构关系推导异质扩散方程的通用形式，分析异质扩散的极限情况，发现非平衡性破缺现象。
摘要：
我们考虑了一种异质扩散方程及其对应的Cattaneo-Vernotte方程通用化形式。该方程是通过连续方程和本构关系在不同随机解释下的异质扩散过程推导而得。系统异质性通过考虑位置依赖的扩散系数引入。给出了概率密度函数和均方位移的精确结果。详细分析了异质扩散的极限情况，并计算了相应的时间平均均方位移。从所得结果中观察到非平衡性破缺现象。
英文摘要：
We consider a heterogeneous diffusion equation and its corresponding generalization to the Cattaneo-Vernotte equation. It is derived by a combination of the continuity equation and the constitutive relation in various stochastic interpretations of the heterogeneous diffusion process. The heterogeneity in the system is introduced by considering a position-dependent diffusion coefficient. Exact results for the probability density function and the mean squared displacement are provided. The limiting case of heterogeneous diffusion is analyzed in detail, and the corresponding time-averaged mean-squared displacement is calculated. From the obtained results, an ergodicity breaking is observed.
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