Transition Path Times in Non-Markovian Activated Rate Processes

Area of Science:

• Chemical Physics
• Molecular Dynamics
• Statistical Mechanics

Background:

• Transition paths are brief molecular excursions between stable conformations.
• Single-molecule experiments reveal insights into reaction dynamics and mechanisms.
• Common models assume memoryless dynamics along the reaction coordinate, but recent work suggests memory effects are important.

Purpose of the Study:

• To investigate how memory effects influence the temporal duration of molecular transition paths.
• To analyze dynamics governed by a generalized Langevin equation with an exponential memory kernel.
• To compare theoretical approximations with numerical simulations.

Main Methods:

• Modeling molecular dynamics using a generalized Langevin equation with an exponential memory kernel.
• Developing and discussing approximate theories for transition path time distributions and means.
• Testing theoretical models against numerical simulations.

Main Results:

• Memory effects significantly alter the temporal duration of transition paths.
• An extreme case of long memory presents challenges for existing approximations.
• Long-memory effects can be explained by coupling the reaction coordinate to an auxiliary degree of freedom.

Conclusions:

• Memory is a critical factor in molecular transition path dynamics.
• Existing theoretical models may not fully capture complex memory effects.
• Coupling to auxiliary degrees of freedom offers a framework for understanding non-Markovian effects in transition paths.