Eternal non-Markovianity is generic for the spin-boson model
arXiv:1701.01292 · doi:10.1103/PhysRevA.95.020101
Abstract
The spin-boson model describes a qubit coupled to a bosonic bath in thermal equilibrium, and is applicable to a wide range of physical contexts. We show that two weak conditions for the qubit evolution to be Markovian (decreasing system distinguishability and divisibility) are violated at all times t>0, except for a measure-zero set of model parameters. Thus, the recently identified phenomenon of `eternal non-Markovianity' is generic for the spin-boson model. Moreover, there can never be more than one strictly positive decoherence rate, even in the Markovian regime. The main result relies on a recent derivation of the exact form of the master equation. We also show that approximations of the spin-boson model in the literature need not exhibit generic eternal non-Markovianity, indicating the presence of corresponding inherent `Markovian' assumptions.
This eprint relies on an 'exact form' for the master equation given recently in https://doi.org/10.1103/PhysRevA.95.020101 . However, the latter result is now in doubt - see the Erratum at https://doi.org/10.1103/PhysRevA.95.069908 . Hence, we have withdrawn the eprint
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