AI 中文总结
该研究针对简谐势阱中耦合热浴的一维奔跑-翻滚粒子，通过奥恩斯坦-乌伦贝克传播子的卷积方法得到位置分布闭式解，修正了早期结果，明确了控制分布转变的无量纲参数，并量化了非平衡特性。
AI 中文摘要
我们研究被简谐势阱约束且耦合到平衡热浴的一维奔跑-翻滚粒子。利用活性自由度与热自由度通过Ornstein-Uhlenbeck propagator（奥恩斯坦-乌伦贝克传播子）的耦合，我们证明位置分布可因式分解为卷积形式，即分解为奥恩斯坦-乌伦贝克分布与非热奔跑-翻滚问题的分布。这得到了闭式结果，通过识别奥恩斯坦-乌伦贝克传播子而非自由扩散传播子为正确核，修正了早期研究的表达式。结果在傅里叶空间和直接朗之万模拟中均得到验证。我们进一步聚焦于定态区域，其特征为两个无量纲参数：束缚长度与 persistence length（ persistence length， persistence长度）之比，以及热扩散与活性扩散之比，这两个参数控制着从非高斯、边界峰值分布到高斯、类平衡极限的转变。能量涨落和与平衡分布的Kullback-Leibler散度量化了受限活性粒子产生的非平衡特性。
英文摘要
We study one-dimensional run-and-tumble particles confined by a harmonic potential and coupled to an equilibrium thermal bath. Exploiting the coupling of active and thermal degrees of freedom through the Ornstein-Uhlenbeck propagator, we show that the position distribution factorizes, as a convolution, into the Ornstein-Uhlenbeck distribution and the distribution of the athermal run-and-tumble problem. This yields closed-form results, correcting expressions from earlier treatments by identifying the Ornstein-Uhlenbeck propagator, rather than the free-diffusion one, as the correct kernel. Results are confirmed both in Fourier space and by direct Langevin simulation. We further focus our analysis on the stationary regime, characterized by two dimensionless parameters--the ratio of trapping to persistence length, and the ratio of thermal to active diffusion--which control the crossover from a non-Gaussian, boundary-peaked distribution to the Gaussian, equilibrium-like limit. Energy fluctuations and the Kullback-Leibler divergence from the equilibrium distribution quantify the resulting non-equilibrium character of the confined active particle.
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