# THE KRAMERS PROBLEM IN THE ENERGY-DIFFUSION LIMITED REGIME

@article{Sancho1998THEKP, title={THE KRAMERS PROBLEM IN THE ENERGY-DIFFUSION LIMITED REGIME}, author={Jos{\'e} M. Sancho and Aldo H. Romero and Katja Lindenberg}, journal={Journal of Chemical Physics}, year={1998}, volume={109}, pages={9888-9900} }

The Kramers problem in the energy-diffusion limited regime of very low friction is difficult to deal with analytically because of the repeated recrossings of the barrier that typically occur before an asymptotic rate constant is achieved. Thus, the transmission coefficient of particles over the potential barrier undergoes oscillatory behavior in time before settling into a steady state. Recently, Kohen and Tannor [D. Kohen and D. J. Tannor, J. Chem. Phys. 103, 6013 (1995)] developed a method…

## 22 Citations

On the generalized Kramers problem with exponential memory friction

- Mathematics, Physics
- 1999

Abstract The time-dependent transmission coefficient for the generalized Kramers problem with exponential memory friction has recently been calculated by Kohen and Tannor [D. Kohen, D.J. Tannor, J.…

On the generalized Kramers problem with oscillatory memory friction

- Chemistry, Physics
- 1999

The time-dependent transmission coefficient for the Kramers problem exhibits different behaviors in different parameter regimes. In the high friction regime it decays monotonically (“nonadiabatic”),…

Numerical simulation of transmission coefficient using c-number Langevin equation

- Physics
- 2003

We numerically implement the reactive flux formalism on the basis of a recently proposed c-number Langevin equation [Barik et al., J. Chem. Phys. 119, 680 (2003); Banerjee et al., Phys. Rev. E 65,…

Memory-induced acceleration and slowdown of barrier crossing.

- Physics, MedicineThe Journal of chemical physics
- 2018

This work studies the mean first-passage time τMFP for the barrier crossing of a single massive particle with non-Markovian memory by Langevin simulations in one dimension and finds barrier crossing to be accelerated for intermediate memory time, while for long memoryTime, barrier crossing is slowed down andτMFP increases with τΓ as a power law τM FP∼τΓ2.

Decay of a metastable state induced by a spin bath.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2011

It is shown that, apart from the usual frequency prefactor and its dynamical modification in the spatial diffusion-limited regime, the rate coefficient contains two other factors, a quantum correction to the dynamical factor resulting from quantum transmission and reflection of the particle at the finite barrier and a quantum corrected Arrhenius factor, which incorporates the effect of thermal saturation.

Time-dependent barrier passage of a non-Ohmic damping system.

- Chemistry, MedicineThe Journal of chemical physics
- 2006

It is shown that the overshooting phenomenon for the passing probability appears in the regime 0<delta<1 and the backflow recrossing over the saddle point is observed, where a nonmonotonous time dependence of the passage probability is detected.

Reactive flux theory for finite potential barriers.

- MedicinePhysical review. E
- 2021

The reactive flux theory for finite barriers is proposed, where the starting point of the trajectories of Brownian particles is removed into a position inside the potential well where the probability distribution can be regarded as an equilibrium one, and the potential barrier is replaced with an equivalent parabolic potential barrier.

Time-dependent barrier passage of one-dimensional fractional damping reactive system

- PhysicsInternational Journal of Modern Physics B
- 2018

The time-dependent barrier passage of a Brownian particle diffusing in the fractional damping environment is studied by using the reactive flux method. Characteristic quantities such as the rate…

From subdiffusion to superdiffusion of particles on solid surfaces.

- Physics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

A numerical and partially analytical study of classical particles obeying a Langevin equation that describes diffusion on a surface modeled by a two-dimensional potential that observes superdiffusion, large-step diffusion, diffusion, and subdiffusion.

Quantum phase-space function formulation of reactive flux theory

- Physics
- 2003

On the basis of a coherent-state representation of the quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee et al.,…

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