手性质量输运过程中的奇扩散与幂律关联

中文摘要 AI 辅助

我们研究了方格上的质量守恒马尔可夫跳跃过程，其中质量以优先旋转方向跳跃，从而同时破坏时间反演对称性和镜面对称性。我们考虑了具有周期边界和开放（反射）边界的封闭系统，后者支持稳态边缘电流。我们证明，由手性输运产生的奇扩散，通常为即使在存在晶格旋转对称性的情况下，非平衡稳态中出现尺度不变的两点密度关联提供了一种机制——这一机制与各向异性跳跃的已知机制在性质上截然不同。我们精确计算了稳态等时密度-密度关联，其表现出代数衰减，对于$|\mathbf{r}| \gg 1$，$C(\mathbf{r}) \sim |\mathbf{r}|^{-4}$。这种代数行为源于扩散张量和迁移率张量的非对角分量之间的相互作用，表明仅手性输运就能在各向同性驱动系统中产生幂律关联。值得注意的是，零波数极限下的结构因子和幂律的振幅对手性有非平凡的依赖。虽然增加手性最初抑制大尺度密度涨落，但超过阈值奇扩散强度后的涨落随手性非单调变化，并形成尖点奇异性。

英文摘要

We study mass-conserving Markov jump processes on a square lattice, where masses hop with a preferred rotational sense, thus breaking both time-reversal and mirror symmetries. We consider closed systems with both periodic and open (reflecting) boundaries, the latter supporting a steady-state edge current. We show that odd diffusion, arising from the chiral transport, generically provides a mechanism for the emergence of scale-invariant two-point density correlations in nonequilibrium steady states even in the presence of lattice rotation symmetry -- a mechanism that is qualitatively distinct from the well-known mechanism of anisotropic hopping. We exactly calculate the steady-state equal-time density-density correlations, which exhibit an algebraic decay, $C(\mathbf{r}) \sim |\mathbf{r}|^{-4}$ for $|\mathbf{r}| \gg 1$. This algebraic behavior results from the interplay between the off-diagonal components of the diffusion and mobility tensors, demonstrating that chiral transport alone can generate power-law correlations in isotropic driven systems. Remarkably, the structure factor in the zero-wavenumber limit and the amplitude of the power laws depend nontrivially on chirality. While increasing chirality initially suppresses large-scale density fluctuations, the fluctuations beyond a threshold odd-diffusion strength vary nonmonotonically with chirality and develop a cusp singularity.

发表机构

• S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国立中心）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

19 pages, 7 figures