The role of external single-well potential, spatially varying temperature, spatially varying trap potential and time varying force on the impurity dynamics

In this paper, we study the role of external parabolic potential, spatially varying temperature, spatially varying trap potential, and time-varying weak signal on the impurities walking from one lattice site to another lattice site. Both temperature and trap potential effects force the system to undergo a phase transition from single well potential to triple well effective potential. In addition, the role of time-varying signal rocks the triple well effective potential and helps the impurities easily surmount the potential barrier. As a result, we study the characterization of stochastic resonance both analytically and numerically.