Barrier-crossing transition-path times for non-Markovian systems

Area of Science:

• Chemical Physics
• Statistical Mechanics

Background:

• Understanding reaction dynamics in complex systems is crucial.
• Non-Markovian friction significantly impacts molecular processes.
• Double-well potentials model many chemical reactions.

Purpose of the Study:

• Investigate the effect of non-Markovian friction on transition-path time.
• Analyze how memory kernels influence reaction coordinate dynamics.
• Develop an accurate theoretical model for transition-path time.

Main Methods:

• Computational simulations were employed.
• Asymptotic theory was used to derive analytical results.
• Single- and multi-exponential memory kernels were considered.

Main Results:

• Non-Markovian friction was found to accelerate transition paths compared to Markovian friction.
• The effect is most pronounced in the low-mass/high-friction regime.
• An asymptotic formula for transition-path time showed good agreement with simulation data.

Conclusions:

• Memory effects in friction play a significant role in reaction dynamics.
• The developed asymptotic formula provides a valuable tool for predicting transition-path times.
• This work offers insights into reaction mechanisms under complex friction conditions.