Computer simulation of quantum effects in Tavis-Cummings model and its applications

We describe computer methods of simulation of Tavis-Cummings based quantum models, and apply those methods to specific tasks, conductivity measurements of atomic excitations in short chains of optical cavities with two-level atoms, C-Sign optical model, and dark states. For the conductivity measurements, we reproduce the dephasing assisted transport and quantum bottleneck effects and show their relation, and study the "which way?" problem. For the C-Sign optical model, we use the model to find optimal parameters of the system to minimize the error. For dark states, we study their collapse due to dephasing noise.