  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.
