Rajarshi Chakrabarti

Department of Inorganic and Physical Chemistry
Indian Institute of Science
Bangalore
India

rajarshi@ipc.iisc.ernet.in

The dynamics of a particle surmounting a barrier is an important and interesting problem in chemistry and physics. In chemistry, chemical reactions are most common examples where one studies the dynamics of barrier crossing along a suitable defined reaction coordinate. While in physics nucleation phenomena, electrical transport etc. involve barrier crossing. In this paper [1] we derive a general expression for the transmission coefficient using the method of reactive flux for a particle coupled to a harmonic bath surmounting a one dimensional barrier. Unlike Kohen and Tannor [2] we use a normal mode analysis where the unstable and the other modes have a complete physical meaning. Importantly our approach results a very general expression for the time dependent transmission coefficient not restricted to overdamped limit. Once the spectral density for the problem is know one can use our formula to evaluate the time dependent transmission coefficient. We have done the calculat! ions with time dependent friction as used by Xie [3] and also the friction used by Kohen and Tannor. Like the formula of Kohen and Tannor our formula also reproduce the results of transition state theory (Arrhenius rate) as well as the Kramer's theory in the limits t $\rightarrow 0$ and t $\rightarrow \infty$ respectively.

References:

1.

R. Chakrabarti (arXiv: cond-mat/0701091v1, 5 Jan 2007).

2.

D. Kohen and D. J. Tannor, J. Chem. Phys 103, 6013 (1995).

3.

S. C. Kou and X. S. Xie, Phys. Rev. Lett. 93, 180603 (2004).