论文标题
驱动的布朗粒子在台阶电位上的传播器
Propagator for a driven Brownian particle in step potentials
论文作者
论文摘要
尽管驱动的布朗颗粒在随机动力学上无处不在，并且通常是随机热力学许多方面的范式模型系统，但完全可以解决的模型却很少且相距甚远。在本文中，我们引入了一种迭代计算方案，类似于静电中的图像方法，如果电势由有限数量的步骤组成，则可以获得传播器。对于单个电势步骤的特殊情况，此方法在一次迭代后会收敛，从而为封闭形式提供了传播器的表达式。在所有其他情况下，迭代会导致近似值的近似值，该近似值比某些特征时间尺度小的次数取决于所执行的迭代次数。该方法也可以应用于像布朗棘轮这样的相关系统，这些系统在其定义中不正式包含阶跃电势，而是施加了由潜在步骤引起的相同的边界条件。
Although driven Brownian particles are ubiquitous in stochastic dynamics and often serve as paradigmatic model systems for many aspects of stochastic thermodynamics, fully analytically solvable models are few and far between. In this paper, we introduce an iterative calculation scheme, similar to the method of images in electrostatics, that enables one to obtain the propagator if the potential consists of a finite number of steps. For the special case of a single potential step, this method converges after one iteration, thus providing an expression for the propagator in closed form. In all other cases, the iteration results in an approximation that holds for times smaller than some characteristic timescale that depends on the number of iterations performed. This method can also be applied to a related class of systems like Brownian ratchets, which do not formally contain step potentials in their definition, but impose the same kind of boundary conditions that are caused by potential steps.
