Microscopic derivation of the Keilson-Storer master equation

- We consider a classical particle bilinearly coupled to a harmonic bath.
- We derive a master equation for the probability density of the particle.
- The master equation is specified by the momentum correlation function.
- We found the correlation function yielding the Keilson-Storer kernel.
- The parameters of the kernel are related to the bath memory time.

We consider a classical particle bilinearly coupled to a harmonic bath. Assuming that the evolution of the particle is monitored on a timescale which is longer than the characteristic bath correlation time, we derive a Markovian master equation for the probability density of the particle. The master equation is fully specified by the time correlation function of the momenta of the particle. We find the functional form of the momentum correlation function which yields the Keilson-Storer master equation (Keilson and Storer, 1952). We show that the parameters of this master equation can directly be related to the characteristic memory time of the bath.