Langevin equation high friction limit

The specific form of the short-time transition probability depends on the type of dynamics one uses to describe the time evolution of the system. For instance, consider a single, one-dimensional particle with mass m evolving in an external potential energy V(q) according to a Langevin equation in the high-friction limit... 

In Kramers theory that is based on the Langevin equation with a constant time-independent friction constant, it is found that the rate constant may be written as a product of the result from conventional transition-state theory and a transmission factor. This factor depends on the ratio of the solvent friction (proportional to the solvent viscosity) and the curvature of the potential surface at the transition state. In the high friction limit the transmission factor goes toward zero, and in the low friction limit the transmission factor goes toward one. 

As an example for a stochastic process consider a system evolving according to the Langevin equation in the high friction limit where inertial effects can be neglected and momenta are not required for the description of the system ... 

If the evolution of the system over times At j>l/ is of interest (thermalization of velocities in each time step— high friction limit ), the friction term is dominant and the inertia term on the left hand side of the Langevin equation can be neglected. Then the equation becomes first order ... 

In this review, we will refer to simulations which use Eq. (2) as the equation of motion as Langevin dynamics (LD) simualtions. Often the high friction or diffusive limit of Eq. (2) is used in simulations ... 

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