Eternal non-Markovianity is generic for the spin-boson model

TL;DR

The paper demonstrates that eternal non-Markovianity is a universal feature in the spin-boson model, showing that the qubit's evolution is inherently non-Markovian for almost all parameter choices, challenging common Markovian assumptions.

Contribution

It proves that eternal non-Markovianity is generic in the spin-boson model and clarifies conditions under which Markovian approximations may fail.

Findings

Eternal non-Markovianity occurs for almost all parameters in the spin-boson model.

There can be at most one positive decoherence rate, even in Markovian regimes.

Common approximations may overlook the inherent non-Markovian nature.

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.