We find an exact series solution for the steady-state probability distribution of a harmonically trapped active Brownian particle in two dimensions in the presence of translational diffusion. This series solution allows us to efficiently explore the behavior of the system in different parameter regimes. Identifying “active” and “passive” regimes, we predict a surprising re-entrant active-to-passive transition with increasing trap stiffness. Our numerical simulations validate this finding. We discuss various interesting limiting cases wherein closed-form expressions for the distributions can be obtained.

中文翻译：

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二维谐波陷阱中活动布朗粒子的稳态

我们找到了一个精确的级数解，用于在平移扩散的情况下二维捕获谐波捕获的有源布朗粒子的稳态概率分布。该系列解决方案使我们能够有效地探索系统在不同参数范围内的行为。识别“主动”和“被动”状态后，我们预计随着陷阱刚度的增加，令人惊讶的重入主动到被动过渡。我们的数值模拟验证了这一发现。我们讨论了各种有趣的极限情况，其中可以获得分布的闭式表达式。