The effect of time-dependent mass on the dynamics of Brownian particles

This research investigates the behavior of particles with time-dependent mass, which increases exponentially toward a limit value, within the framework of Brownian motion. The study employs the Langevin model to analyze the effects on mean squared displacement and velocity distributions of these particles. Solutions are provided specifically for the white noise case, examining the changes in the mean squared displacement and mean squared velocity as the mass increases. Consistent with physical reality, it has been observed that an increase in mass results in a reduced rate of displacement of particles from their initial position. As a result of the fluctuation–dissipation theorem, it is demonstrated that the change in mass affects the equilibrium state between the intensity of the external force and the damping parameter. Theoretical results are evaluated through graphical representations, offering a detailed discussion on the impact of mass variation on particle dynamics. This approach provides significant insights into how time-dependent mass variations influence particle motion. Graphical abstract