Dissipative dynamics from a stochastic perspective

The stochastic description of dissipative dynamics for both quantum and classical systems is revisited by using Itô calculus. A procedure to work out the master equation for linear systems based on this scheme is outlined. For the Caldeira-Leggett model it is shown that the master equation describing pure dephasing is Markovian-like and the solution is given. The Caldeira-Leggett master equation for Ohmic dissipation, which is valid at high temperatures, is derived.