Graduate Noise in Landau–Zener transition

[kelly0303]

Hello! I want to simulate a 2 level system in which the 2 levels are connected by an off-diagonal Hamiltonian term. I can linearly tune the distance between the 2 levels and thus I can transfer population from one to the other using a Landau–Zener transition. However, I want to add noise to this linear sweep. In my case the splitting between the 2 levels is adjusted by changing a magnetic field, but in practice the value of the magnetic field has some noise associated to it (due to noise in the current in the coils used to produce the magnetic field). I want to emphasize that that the noise leads to (small) changes in the magnetic while I do the linear sweep. So not only that the magnetic field is slightly different between different experimental runs, but it varies as a function of time while I perform the sweep. I would like to model this numerically and see the effect of different kind noise amplitude but I am not sure how to start. What is the easiest way to model noise in general and how should I proceed for more realistic representations of noise (any paper/book about this would be really appreciated, too)? In the end I would like to solve the Schrödinger equation associated to this 2x2 system in the presence of noise and extract the transition probability. Thank you!