Scale invariance in the dynamics of a non-magnetic ellipsoidal particle lying on a granular thermal bath fluidized

We studied the Brownian motion of a non-magnetic ellipsoidal particle lying on a granular thermal bath fluidized using a combination of an alternating magnetic field and a constant magnetic field. Using Fourier analysis (FA), we recently found scale invariance in the particle position time series at different effective temperatures. In contrast, particles in the granular bath do not present scale invariance when the effective temperature lowers. In the present contribution, we extended the study to consider two different sizes of the ellipsoidal particle and different values of the constant magnetic field for the thermal bath. In all cases, the Fourier power spectra reveal scale invariance. The time series of the ellipsoidal particle positions in x-direction and the angular time series constructed from rotational motions follow a power law, P(f) ∝ 1/ f^β with β≈2, indicating Brownian-like motion. In the absence of a constant magnetic field, the scale invariance property is valid only for high values of the oscillating magnetic field.  In this way, using time series analysis techniques, the characterization of Brownian paths' emergence in this active matter model is achieved.