Escape or switching at short times

In the standard Arrhenius picture [S. Arrhenius, Z. Phys. Chem., Stoechiom. Verwandtschaftsl. 4, 226 (1889); L. Néel, Ann. Geophys. (C.N.R.S.) 5, 99 (1949)] of thermal switching or escape from a metastable to a stable state, the escape probability per unit time Ps (t) decreases monotonically with time t as Ps (t) ∼ e-t/τD, where the decay time τD = τ0 eU/kB T, with U the energy barrier, kB T the thermal energy, and τ0 the time between escape attempts. Here, we extend the Arrhenius picture to shorter times by deriving general conditions under which Ps (t) is peaked rather than monotonic, and showing that in the simplest scenario the peak time τP diverges with τD as ln (τD). © 2005 The American Physical Society.