  Kinetic aspect of Landauer's blowtorch 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 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.
