  A colloidal suspension of active Brownian particles (ABPs) driven by
controllable forces into directed or persistent motions can serve as a model
for understanding the biological systems. Experiments and numerical simulations
are established to investigate the motions of an ABP, a single, induced-charge
electrophoretic (ICEP) metallic Janus particle, confined in a quadratic
potential well. On the one hand, 1-D position histograms of the trapped active
particle, behaving differently from that of a Boltzmann distribution, reveal a
splitting from a single peak of the ABP positional distribution to a bimodal
distribution. Decoupling the thermal and non-thermal contributions from the
overall histogram is non-trivial. However, the two contributions can be
examined by convoluting numerically generated thermal and non-thermal
contributions into a full histogram. On the other hand, temporal fluctuations
analyzed by the power spectral density (PSD), reveal two unique frequencies
characterizing the stiffness of the trap and the rotational diffusion of the
particle, respectively. Connections between the spatial and temporal
fluctuations are obtained by the separate analysis of the temporal and spatial
fluctuations of an ABP trapped in a quadratic potential well. This study
reveals how thermal and nonthermal fluctuations play against each other in a
confined environment.
