A perfect probe: Resonance of underdamped scaled Brownian motion

¹ Faculty of Civil Engineering and Mechanics/Faculty of Science, Kunming University of Science and Technology Kunming 650500, China
² Paul M. Rady Department of Mechanical Engineering and Department of Physics, University of Colorado Boulder, CO 80309-0427, USA
³ School of Physics and Information Engineering, Zhaotong University - Zhaotong 657000, China

^(a) zchh2009@126.com (corresponding author)

Received: 26 July 2021
Accepted: 23 December 2021

Abstract

We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function and mean squared displacement of a single particle, we find that for the steady state, diffusions are free ballistic motion in short time, become the transitions between superdiffusion and subdiffusion in intermediate time, and converge to zero at long times. Via the power spectrum density corresponding to the transitions between superdiffusion and subdiffusion, we find that there exists a nontrivial resonance. For interacting particles, we find that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of different coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles.