Effect of Landauer's blow torch on the equilibration rate in a bistable potential

Abstract

The kinetic aspect of Landauer's blow-torch effect is investigated for a model double-well potential with localized heating. Using the supersymmetric approach, we derive an approximate analytical expression for the equilibration rate as a function of the strength, width, and the position of the hot zone, and the barrier height. We find that the presence of the hot zone enhances the equilibration rate, which is found to be an increasing function of the strength and width of the hot zone. Our calculations also reveal an intriguing result, namely, that placing the hot zone away from the top of the potential barrier enhances the rate more than when it is placed close to it. A physically plausible explanation for this is attempted. The above analytical results are borne out by detailed numerical solution of the associated Smoluchowski equation for the inhomogeneous medium.