We study the dynamics of the separation (gap) between a pair of interacting run and tumble particles moving in one dimension in the presence of additional thermal noise. On a ring geometry the distribution of the gap approaches a steady state. We analytically compute this distribution and find that this is exponentially localised in space, in contrast to the ‘jammed’ configuration, seen earlier in the absence of thermal noise. We also study the relaxation which is an exponential in time, characterised by a time scale τ r . We observe that this time scale undergoes a crossover from a size independent value to a size dependent form with increasing size l of the ring. We study the full eigenvalue spectrum of the evolution operator ##IMG## [http://ej.iop.org/images/1751-8121/53/34/345003/aab9cf3ieqn1.gif] {$\mathcal{L}$} and find that the spectrum can be classified into four sectors depending on the symmetries of ##IMG## {...}

中文翻译：

---

一维两个相互作用的运行和滚动粒子的间隙统计

我们研究了在存在附加热噪声的情况下，一对相互作用的运行和滚动颗粒在一个维度上移动之间的分离（间隙）动力学。在环形几何体上，间隙的分布接近稳态。通过分析计算该分布，发现该分布在空间上呈指数分布，这与先前在没有热噪声的情况下看到的“堵塞”配置相反。我们还研究了时间上呈指数形式的弛豫，其特征在于时间标度τr。我们观察到，随着环的尺寸l的增加，该时间标度经历了从尺寸无关值到尺寸依赖形式的交叉。我们研究了进化算子## IMG ## [http://ej.iop.org/images/1751-8121/53/34/345003/aab9cf3ieqn1的完整特征值谱。