Control of diffusion and transition phenomena in a periodic system with temporal symmetry breaking

Diffusion of Brownian particle in a periodic system with temporal symmetry breaking is investigated, where the temporal symmetry breaking is caused by two periodic forces with different frequencies. The Brownian particle is driven by a harmonic noise generated via a RLC circuit subjected to an additive Gaussian noise. Our research results indicate that: (i) There are three types of diffusions in the system: superdiffusion, normal diffusion, and subdiffusion, depending on two controllable parameters ( \(\Gamma \) $\mathrm{\Gamma }$ and \(\Omega \) $\mathrm{\Omega }$ ) of the RLC circuit. In other words, we can obtain the diffusion we desire through adjusting the parameters of the RLC circuit. (ii) There are two transition phenomena in the system: one involves with the dependence of diffusion index of the particle on \(\Gamma \) $\mathrm{\Gamma }$ , the other does on \(\Omega \) $\mathrm{\Omega }$ . The two transitions are caused by amplitudes of the two periodic signals in the periodic system. These research results will be of great significance for controlling anomalous diffusion of Brownian particle and improving operating performance of Nano-Brownian motors.