Evolution of quantum systems is described by Lindblad-Franke equation for density matrix. We seek pointers of this equation: such density matrices (i.e. quantum states) that don’t change over time. Pointers are believed to be the final step in evolution of density matrices of open quantum systems and, consequently, they are expected to reveal decoherence, i.e. the process of system's loss of quantum properties and gaining classical ones.
To start with, we look at the pointers of the Liouville–von Neumann part of the equation and next we find how they change after “turning on” the Lindblad-Franke part. It is implemented by means of perturbation theory. The cases of non-degenerate and degenerate Hamiltonians are studied. We further apply our method to concrete physical setups.
This work is done in collaboration with A.A.Andrianov, M.V.Ioffe and O.O.Novikov.