Thermally activated escape rate and dynamics of a particle under a harmonic potential

In this paper, we study the dynamics of particles along a semiconductor layer by imposing a confinement potential assisted by both thermal noise strength D and trap potential φ. By applying a nonhomogeneous cold temperature alongside the uniform background temperature, the system is driven towards a phase transition. When a weak signal is pass across a semiconductor layer, the thermally activated particles become easily hop from one lattice site to another lattice site. We perform a numerical simulation of the trajectory of a particle under a harmonic potential represents a bistable and tristable effective potential as a function of thermal noise. As a result, at an optimal level of noise, the particle synchronizes with a weak periodic signal.