 03354 Jan Derezinski, Vojkan Jaksic
 On the nature of Fermi Golden Rule for open quantum systems
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Jul 30, 03

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Abstract. We consider a general class of models consisting of a small quantum
system $\cS$ interacting with a reservoir $\cR$. We compare three
applications of 2nd order perturbation theory (the Fermi Golden Rule)
to the study of such models:
(1) the van Hove (weak coupling) limit for the dynamics reduced
to ${\cal S}$;
(2) the Fermi Golden Rule applied to the Liouvilleanan argument
that was used in recent papers on the return to equilibrium;
(3) the Fermi Golden Rule applied to the socalled CLiouvillean.
These three applications lead to three Level Shift Operators.
As our main result, we prove that if the reservoir $\cR$ is thermal
(if it satisfies the KMS condition), then the Level Shift Operator
obtained in (1) (often called the Davies generator) and the Level Shift
Operator constructed in (2) are connected by a similarity transformation.
We also show that the Davies generator coincides with the Level Shift
Operator obtained in (3) for a general $\cR$.
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