二维泊松型跑动-翻滚粒子的超扩散
Hyperdiffusion of Poissonian run-and-tumble particles in two dimensions
AI总结：
研究二维泊松型跑动-翻滚粒子在复杂环境中的局域化动力学，通过时空耦合技术推广Montroll-Weiss公式，发现短中时间尺度下超越弹道极限的超扩散标度。
摘要：
我们研究了二维中非相互作用的泊松型跑动-翻滚粒子（RTPs），其速度方向由任意圆形分布 $Q(ϕ)$ 控制。据报道，RTP型活性传输在拥挤和无序环境内会发生局域化，但其非平衡动力学，尤其是在中间时间尺度上，尚未得到解析阐明。在此，从标准（单态）RTPs出发，我们通过以马尔可夫方式拼接过阻尼布朗运动，构建了局域化（双态）RTPs。利用连续时间随机游走理论中的时空耦合技术，我们以傅里叶系数 $Q_ν$ 的可分解形式推广了Montroll-Weiss公式，并揭示了位移矩 $\left \langle \mathbf{r}^{2μ}(t) \right \rangle$ 依赖于有限角动量 $Q_ν$（$|ν|\leq μ$）。基于这一发现，我们提供了（i）单态RTPs的速度重定向角分布，以及（ii）双态RTPs在所有时间尺度上的 $\left \langle \mathbf{r}^{2}(t) \right \rangle$。特别地，我们发现了依赖于初始动态状态的 $\left \langle \mathbf{r}^{2}(t) \right \rangle$ 的复杂时间演化，并且显著地，在短时间和中间时间尺度内检测到了超扩散标度 $\left \langle \mathbf{r}^{2}(t) \right \rangle \propto t^{β(t)}$，其反常指数为 $2<β(t)\leq 3$。我们的工作表明，复杂系统内出现的局域化甚至能将活性传输的扩散速率提升至超越弹道极限。
英文摘要：
We study non-interacting Poissonian run-and-tumble particles (RTPs) in two dimensions whose velocity orientations are controlled by an arbitrary circular distribution $Q(ϕ)$. RTP-type active transport has been reported to undergo localization inside crowded and disordered environments, yet its non-equilibrium dynamics, especially at intermediate times, has not been elucidated analytically. Here, starting from the standard (one-state) RTPs, we formulate the localized (two-state) RTPs by concatenating an overdamped Brownian motion in a Markovian manner. Using the space-time coupling technique in continuous-time random walk theory, we generalize the Montroll-Weiss formula in a decomposable form over the Fourier coefficient $Q_ν$ and reveal that the displacement moment $\left \langle \mathbf{r}^{2μ}(t) \right \rangle$ depends on finite angular moments $Q_ν$ for $|ν|\leq μ$. Based on this finding, we provide (i) the angular distribution of velocity reorientation for one-state RTPs and (ii) $\left \langle \mathbf{r}^{2}(t) \right \rangle$ over all timescales for two-state RTPs. In particular, we find the intricate time evolution of $\left \langle \mathbf{r}^{2}(t) \right \rangle$ that depends on initial dynamic states and, remarkably, detect hyperdiffusive scaling $\left \langle \mathbf{r}^{2}(t) \right \rangle \propto t^{β(t)}$ with an anomalous exponent $2<β(t)\leq 3$ in the short- and intermediate-time regimes. Our work suggests that the localization emerging within complex systems can increase the dispersion rate of active transport even beyond the ballistic limit.
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