Moving in the force-free potential and the tilted periodic potential, the diffusion of the under-damped particle subjected to correlated Lvy noise, i.e. the harmonic velocity Lvy noise, is investigated in this paper. We find that the underlying negative time correlation, especially the strong one, distinctly collides with the long-tailed nature of the noise, which results in a multi-diffusive process in the force-free potential. In the tilted periodic potential, strong correlation means that the transport of particle cannot be separated as the typical locked state and running state in coordinate space. Correspondingly, the anomalous diffusion in the tilted periodic potential does not hold anymore, which becomes a normal shape at asymptotic timescale.

本文研究了在无力势和倾斜周期势中运动的欠阻尼粒子在相关Lvy噪声即谐波速度Lvy噪声下的扩散。我们发现潜在的负时间相关性，尤其是强相关性，与噪声的长尾性质明显冲突，导致无力势中的多重扩散过程。在倾斜周期势中，强相关性意味着粒子的输运不能作为坐标空间中典型的锁定态和运行态分开。相应地，倾斜周期势中的异常扩散不再成立，在渐近时间尺度上变为正常形状。