| Abstract: |
| Brownian motion in a periodic potential arises in contexts ranging from solid-state physics to molecular motors to communication theory. In such contexts, stochastic effects can be exploited using the remarkable fact that an (additional) arbitrarily small biasing force induces a nonzero steady state particle current in the presence of noise. In this talk we discuss this force-current relationship under the assumption of a constant biasing force; in the 1-dimensional case we show that the small-noise asymptotics are completely determined by a certain persistent homology barcode determined by the underlying potential and the biasing force. Using this topological viewpoint we also discuss the higher-dimensional phenomenon of negative resistance which can occur in the force-current relationship. |
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