Time evolution of spin-boson system for different effective spectral density functions

In this paper we firstly obtain two kinds of effective spectral density functions by setting the cut-off frequencies of baths be infinite and finite. Secondly, we investigate the reduced dynamics of open qubits in four kinds of systems constructed with the basic spin-boson model. It is shown that the qubit has different dynamics governed by the two kinds of spectral density functions. In addition, we obtained that a qubit coupled to an intermediate harmonic oscillator has longer decoherence and relaxation times as they are coupled to a common bath than to their respective baths. In solving the dynamics of qubits we use a numerically exact algorithm, iterative tensor multiplication algorithm based on the quasiadiabatic propagator path integral scheme.