Resonant diffusion of Debye Brownian oscillators in weakly tilted periodic potentials

We investigate the diffusive dynamics of Debye Brownian oscillators in tilted periodic potentials. These oscillators are driven by Debye-type noise characterized by a spectral density with a hard cutoff at high finite frequencies. For force-free Debye Brownian oscillators, we derive an explicit expression for the self-oscillating frequency of the velocity autocorrelation function. When subjected to weakly tilted forces in a periodic potential, the oscillators exhibit a resonant diffusion phenomenon. Specifically, the effective diffusion coefficient reaches its maximum when the self-oscillating frequency matches the frequency of local wells in the tilted periodic potential. We attribute this resonance diffusion to the competition between fluctuation and friction. At resonance, the effective temperature exhibits a more pronounced increase compared with the effective friction. As the tilted force increases, the resonant diffusion phenomenon gradually disappears. This is accompanied by a monotonic decrease in the effective diffusion coefficient, caused by stronger friction with increasing cutoff frequency. This study provides insights into diffusive dynamics in realistic systems with limited resources, which may have implications for understanding various physical processes involving Brownian motion in complex environments.