# Coexistence of absolute negative mobility and anomalous diffusion

## TL;DR

This study demonstrates through numerical simulations that absolute negative mobility can coexist with various types of anomalous diffusion in a driven Brownian particle system, revealing complex transport behaviors.

## Contribution

The paper provides the first comprehensive numerical evidence that absolute negative mobility and multiple forms of anomalous diffusion can occur simultaneously in a single model.

## Key findings

- Absolute negative mobility coexists with anomalous diffusion types.
- The model exhibits coherent motion, ballistic diffusion, subdiffusion, superdiffusion, and hyperdiffusion.
- Numerical results support the coexistence across different physical regimes.

## Abstract

Using extensive numerical studies we demonstrate that absolute negative mobility of a Brownian particle (i.e. the net motion into the direction opposite to a constant biasing force acting around zero bias) does coexist with anomalous diffusion. The latter is characterized in terms of a nonlinear scaling with time of the mean-square deviation of the particle position. Such anomalous diffusion covers "coherent" motion (i.e. the position dynamics x(t) approaches in evolving time a constant dispersion), ballistic diffusion, subdiffusion, superdiffusion and hyperdiffusion. In providing evidence for this coexistence we consider a paradigmatic model of an inertial Brownian particle moving in a one-dimensional symmetric periodic potential being driven by both an unbiased time-periodic force and a constant bias. This very setup allows for various sorts of different physical realizations.