Qubit Decoherence and Non-Markovian Dynamics at Low Temperatures via an   Effective Spin-Boson Model
  Quantum Brownian oscillator model (QBM), in the Fock-space representation, can be viewed as a multi-level spin-boson model. At sufficiently low temperature, the oscillator degrees of freedom are dynamically reduced to the lowest two levels and the system behaves effectively as a two-level (E2L) spin-boson model (SBM) in this limit. We discuss the physical mechanism of level reduction and analyze the behavior of E2L-SBM from the QBM solutions. The availability of close solutions for the QBM enables us to study the non-Markovian features of decoherence and leakage in a SBM in the non-perturbative regime (e.g. without invoking the Born approximation) in better details than before. Our result captures very well the characteristic non-Markovian short time low temperature behavior common in many models. 
K. Shiokawa and B. L. Hu