Peculiarities of parabolic-barrier penetrability and thermal decay rate with the quantum diffusion approach

Abstract

With the quantum diffusion approach, the passing probability through the parabolic barrier is examined in the limit of linear coupling in the momentum between the collective subsystem and environment. The dependencies of the penetrability on time, energy, and the coupling strength between the interacting subsystems are studied. The quasistationary thermal decay rate from a metastable state is considered in the cases of linear couplings both in the momentum and in the coordinate.

Non-Markovian dynamics with fermions

“…For the sake of simplicity, in further analytical calculations we use the dissipative kernels (14). For the average occupation number n(t), one can obtain (see Appendix A):…”

“…We use the Langevin approach [10][11][12][13][14] which is widely applied to find the effects of fluctuations and dissipations in macroscopical systems. The Langevin method in the kinetic theory significantly simplifies the calculation of nonequilibrium quantum and thermal fluctuations and provides a clear picture of the dynamics.…”

Probability of passing through a parabolic barrier and thermal decay rate: Case of linear coupling both in momentum and in coordinate

“…[20], the value of β i depends on the four roots and the limits at α = 0 or g = 0 are not trivial. One can show that, at α = 0, Eqs.…”

“…[20], in Sec. II we briefly derive the quantum and non-Markovian Langevin equations for the collective coordinate and canonically conjugated momentum for the case of general linear coupling.…”

“…In Ref. [20], we studied the limit of a linear coupling in momentum. Here, we investigate the general case of a linear coupling both in momentum and in coordinate between the relevant collective coordinate and the heat bath.…”