The possibility of observing stochastic resonance (SR) in a periodic potential without a static bias, driven by noise and an oscillating field, is investigated in both limits of damping. It is shown from the matrix continued fraction method that, although an underdamped Brownian particle moving in a periodic potential displays a dynamical resonance facilitated by noise, there is no conventional SR irrespective of damping. The reason such SR cannot be observed in an overdamped regime is demonstrated by a hopping model. Due to the unbound motion in the periodic potential, transition probability decays algebraically and there is no persistent synchronized hopping. However, the noise-induced enhancement of the diffusion constant related to escape rate enhancement exhibits an SR-like behavior. A comparison with the dynamics on a circle as a different example of an unbound system is given. [References: 20]
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