Transition State Theory Rate in Nonlinear Environment: the Under-damping Case*

摘要: We investigate the escape behavior of systems governed by one-dimensional nonlinear Kramers' equation ∂W/∂t = −v∂W/∂x + (f'(x)/m)(∂W/∂v) γ∂(vW)/∂v +(γkBT/m)(∂2Wμ/∂v2), where f(x) is a metastable potential and μ an anomalous exponent. obtain expression for transition state theory rate, whose predictions are in good agreement with numerical simulations. The results exhibit anomalies due to nonlinearity W that TST rate grows T drops as becomes large at fixed T. Indeed, particles subdiffusive media (μ > 1) can over barrier only when above critical value, while there does not exist this confinement superdiffusive < 1).