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System-Bath Interaction

Assume a `bath' of bosonic modes $ Q$ (the index $ Q$ contains all quantum numbers of that mode) with creation operator $ a_Q^{\dagger}$. The simplest interaction between the two-level system and the bath is linear in $ a_Q^{\dagger}$ and $ a_Q$ and can be written with coupling constant vectors $ {\bf g}_Q(t)$,
$\displaystyle H_{SB}(t)$ $\displaystyle \equiv$ $\displaystyle \hat{\bf A}(t) \vec{\sigma}\equiv
\sum_Q \left( {\bf g}_Q(t) a_Q^{\dagger} + {\bf g}_Q^{\dagger}(t) a_Q\right)\vec{\sigma}.$ (110)

Note that $ \hat{\bf A}(t)$ can be regarded as a fluctuating (quantum operator) pseudo magnetic field.

Tobias Brandes 2004-02-18