Master Equation under a classical fluctuating noise I have a system as a qubit with Hamiltonian
$H_S = \frac{\Delta}{2}\sigma_z$
The interaction Hamiltonian is
$H_I = \frac{V(t)}{2}\sigma_z$ where $V(t)$ is a stochastic fluctuating variable. One can for example assume it as a random telegraph noise(RTN). In this case, what is the general prescription to write down the master equation for the qubit?
 A: The book by Klyatskin discusses general functional methods for dealing with gaussian and telegraph noises.
However, let me make a few general remarks:

*

*Telegraph noise is not delta-correlated (white), which means that one would get an integral equation, rather than usual master equation.

*Including noise as an external force, without taking into account its respose to the qubit dynamics, breakes the fluctuation-dissipation theorem. Thus, the resulting equation will not contain dissipative/relaxation terms (again, it is not a master equation, properly speaking).

*Writing a master equation for a two-level system is a bit of overkill, since Bloch equations are enough for a two-level system.

A: There is a procedure outlined here: A. A. Budini, "Non-Markovian Gaussian dissipative stochastic wave vector", Phys. Rev. A 63, 012106 (2000).
You basically take an ensemble average over the noise realizations, and use some techniques from functional calculus. It is based on Gaussian noises, but you can extend it to non-Gaussian noises too, however you will not reach a Lindblad-like master equation.
You can also see my paper, which is based on the above reference: https://arxiv.org/abs/1612.02628
The derivation is in section III.B (it is severely shortened though), and the key point is Eq. 49. If you want to use non-Gaussian noises, that equation has a generalization in
F. Moss and P. McClintock, Noise in Nonlinear Dynamical Systems:
Volume 1, Theory of Continuous Fokker-Planck SystemsRef. (Look for Eq. 9.4.1).
