Anomalous transport in periodic systems driven by active fluctuations
This dissertation investigates the transport of Brownian particles driven by active fluctuations in periodic potential landscapes. Unlike thermal noise, active fluctuations break detailed balance and violate the fluctuation-dissipation theorem. They model self-propulsion mechanisms and active-bath interactions in biological and synthetic micro-systems. By focusing on white Poisson shot noise with non-Gaussian amplitude statistics, this work systematically uncovers the mechanisms governing three major transport anomalies: giant transport enhancement, absolute negative mobility, and the ratchet effect. Combining Monte Carlo simulations with analytical modeling, this work demonstrates that active fluctuations adhering to a bidirectional skew-normal amplitude distribution enhance directed velocity compared to the free-particle by several orders of magnitude. This giant transport enhancement is fully quantified via a phenomenological jump-relaxation model that decouples particle displacement into instantaneous stochastic jumps and deterministic relaxation towards potential minimum. Extending this model to inertial dynamics reveals that finite particle mass m acts as a dynamic control parameter capable of strengthening, weakening, constructively inducing, or completely suppressing transport enhancement depending on noise variance. Furthermore, an ultra-minimal model for absolute negative mobility is established in a one-dimensional, purely overdamped system, showing that discontinuous shot noise drives transport opposite to an applied bias without requiring particle inertia, nonlinearity of spatially periodic potential, or explicit time-dependent periodic driving. Conversely, under an alternative scaling of the average stochastic force, an asymmetric distribution of fluctuation amplitudes generates net directed transport through a tilting ratchet effect in the zero-bias limit.