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DY: Fachverband Dynamik und Statistische Physik

DY 32: Posters DY - Statistical Physics, Brownian Motion and Nonlinear Dynamics

DY 32.12: Poster

Tuesday, March 23, 2021, 16:30–19:00, DYp

Propagator for a driven Brownian particle in step potentials — •Volker Weißmann, Matthias Uhl, and Udo Seifert — II. Institute for Theoretical Physics , University of Stuttgart

Although driven Brownian particles are ubiquitous in stochastic dy- namics and often serve as paradigmatic model systems for many as- pects of stochastic thermodynamics, fully analytically solvable models are few and far between. In [1], 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 con- verges after one iteration, thus providing an expression for the prop- agator 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 Brow- nian 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.

[1]: Matthias Uhl et al 2021 J. Phys. A: Math. Theor. 54 065002 https://doi.org/10.1088/1751-8121/abc21f