|Ph.D Thesis||Department of Physics|
|Supervisors:||Prof. Emeritus Ron Amiram|
|Prof. Orenstein Meir|
We examine the validity of applying the assumptions in the Master equation, by using the Resolvent method and introducing the Feynmann diagrams. The Factorization approximation is addressed, and justified in the sense of a small expansion parameter. The results are demonstrated for a system of two states in a reservoir. It is shown that the Markoff ansatz is equivalent to assuming that the system self-energy can be considered as a constant.
We investigate the dynamics of a composite system, made of two coupled subsystems, when only one of them is interacting significantly with the environment. The equations of motion for the reduced density matrix of the composite system are derived using only the Factorization approximation, without appealing to the Markoff ansatz. These equations are compared with the conventional ad hoc approach, which assumes that the relaxation terms of the equations of motion of the composite system can be borrowed from the Master equation of the single subsystem that is interacting with the reservoir. For demonstration we consider a system of a three levels’ atom including intrinsic coupling. The time evolution and steady state of the system are studied by using the Laplace transform method.
We analyze a system of two coupled microcavities, where one of them is in contact with the environment. We derive the proper Master equation, which guarantees the whole system to reach thermal equilibrium at steady state. We investigate the dissipations in the Jaynes-Cumming model, for the two cases of leaky atom and leaky cavity, where the equations of motion for the populations and coherences of the system states are derived.