Freezing Transition in the Barrier Crossing Rate of a Diffusing Particle.

@article{Sabhapandit2020FreezingTI,
  title={Freezing Transition in the Barrier Crossing Rate of a Diffusing Particle.},
  author={Sanjib Sabhapandit and Satya N. Majumdar},
  journal={Physical review letters},
  year={2020},
  volume={125 20},
  pages={
          200601
        }
}
We study the decay rate θ(a) that characterizes the late time exponential decay of the first-passage probability density F_{a}(t|0)∼e^{-θ(a)t} of a diffusing particle in a one dimensional confining potential U(x), starting from the origin, to a position located at a>0. For general confining potential U(x) we show that θ(a), a measure of the barrier (located at a) crossing rate, has three distinct behaviors as a function of a, depending on the tail of U(x) as x→-∞. In particular, for potentials… 

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