标记活性粒子：缓变外势中的概率分布由爱因斯坦关系得到的有效温度决定
Tagged active particle: probability distribution in a slowly varying external potential is determined by effective temperature obtained from the Einstein relation
AI总结：
本研究推导了相互作用活性粒子系统中缓变外势下标记活性粒子的位置分布，证明其有效温度与爱因斯坦关系定义的一致，且适用范围超出线性响应区，通过模拟验证了理论，并指出理论在运动诱导相分离附近失效。
摘要：
我们在相互作用活性粒子系统中，推导了空间缓变外势下单个标记活性粒子的位置分布函数。该标记粒子的分布具有玻尔兹曼分布的形式，但用有效温度替代了热浴温度。我们证明，进入标记粒子分布的有效温度，与通过爱因斯坦关系定义的有效温度相同，即等于自扩散系数与标记粒子迁移率系数的比值。这表明，这种通过涨落-耗散比定义的有效温度，其适用范围超出了线性响应区域。我们通过计算机模拟验证了理论结果。当活性系统中出现额外的大长度尺度时，我们的理论不再成立。该长度尺度与趋近运动诱导相分离时出现的长波密度涨落相关。
英文摘要：
We derive a distribution function for the position of a tagged active particle in a slowly varying in space external potential, in a system of interacting active particles. The tagged particle distribution has the form of the Boltzmann distribution but with an effective temperature that replaces the temperature of the heat bath. We show that the effective temperature that enters the tagged particle distribution is the same as the effective temperature defined through the Einstein relation, i.e. it is equal to the ratio of the self-diffusion and tagged particle mobility coefficients. This shows that this effective temperature, which is defined through a fluctuation-dissipation ratio, is relevant beyond the linear response regime. We verify our theoretical findings through computer simulations. Our theory fails when an additional large length scale appears in our active system. This length scale is associated with long-wavelength density fluctuations that emerge upon approaching motility-induced phase separation.
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