Non-Markovian diffusion over a parabolic potential barrier: influence of the friction-memory function

B. Yilmaz (1, 2) , S. Ayik (3) , Y. Abe (4) , D. Boilley (5, 6)

1 Physics Department, Ankara University
2 Physics Department
3 Physics Department, Tennessee Technological University
4 RCNP - Research Center for Nuclear Physics
5 GANIL - Grand Accélérateur National d'Ions Lourds
6 UNICAEN - Université de Caen Normandie

The over-passing probability across an inverted parabolic potential barrier is investigated according to the classical and quantal generalized Langevin equations. It is shown that, in the classical case, the asymptotic value of the over-passing probability is determined by a single dominant root of the characteristic function, and it is given by a simple expression. The expression for the over-passing probability is quite general, and details of dissipation mechanism and memory effects enter into the expression only through the dominant root of characteristic equation

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique Nucléaire Théorique [nucl-th]

B. Yilmaz, S. Ayik, Y. Abe, D. Boilley. Non-Markovian diffusion over a parabolic potential barrier: influence of the friction-memory function. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2008, 77, pp.011121. ⟨10.1103/PhysRevE.77.011121⟩. ⟨in2p3-00202731⟩