Varyasyonel matris çarpım durumları metodunun bağlı kovuk zincirinde kuantum dinamiğine uygulanması

Matrix product state (MPS) representation is an alternative way to describe a quantum many body system on a one dimensional lattice by means of an interconnected local tensor array. The exponential growth of the Hilbert space of a quantum many body system is a major limitation in numerical calculations. In variational matrix product state (VMPS) method, the Hilbert space of a system is represented by a reduced number of basis vectors, therefore allowing the simulation of larger systems. We have applied VMPS method to a model of coupled quantum cavity arrays. In our model in one of the cavities, there is a two level system (TLS) interacting with the cavity mode. We have studied the system in both the so-called rotating wave approximation (RWA) and beyond including counter rotating wave (CRW) terms in Rabi model. We have calculated the ground state particle distributions of the system with different coupling strengths. Using the Suzuki-Trotter decomposition, we have investigated time dependent dynamics of emission from the TLS within RWA and beyond. Finally, scattering of a Gaussian shaped pulse from a TLS is simulated within RWA and including CRW terms.