Blowtorch Effect On The Escape And Equilibration Rates For The Hopping Model

In bistable systems the transition kinetics between two locally stable states can be alteredrnby heating locally one of the stable states (using blow-torch). As a model for diffusion inrna non-homogeneous medium, we consider the hopping model. The kinetic aspect of blowtorchrneffect is investigated for a model double-well potential with localized heating. That is,rnwe analyze the relaxation behavior of a bistable system when the background temperaturernprofile is non-homogeneous. Using Brinkman’s method, we derive the general and analyticrnexpressions for the escape and equilibration rates of the system as a function of the strength,rnwidth, and the position of the hot locality, the barrier height and the pit potential of trapsrnfor the model that we consider.rnOur result shows that the presence of the hot locality enhances the escape rate from thernwell where it is placed and retards the escape rate from the other well. Our work also showsrna remarkable result in relation to the position of the hot locality in that placing the hotrnlocality mid way between the top and bottom of the well has the largest enhancing effect onrnthe escape rate from the hot zone than any other position. This result is similar to the workrnof Solomon Fekade and Mulugeta Bekele for the case of Landauer’s heated pipe model[1].rnMoreover, the escape and equilibration rates of the system become decreasing functions ofrnthe barrier height and the pit potential of traps

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