N-level systems in contact with a singular reservoir. II

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Abstract
We study an N‐level system coupled linearly to an infinite quasifree Fermi or Bose reservoir in the vacuum state or in a state corresponding to an arbitrary temperature. We show that the singular reservoir limit can be performed in the vacuum state and at infinite temperature, thus leading to a completely positive Markovian reduced time evolution for the system, which, in the infinite temperature case, preserves the central state. On the other hand, no such limit is possible for KMS states (finite temperature) and at zero temperature. Some extension to norm‐continuous semigroups of an infinite‐dimensional B (H) is possible.

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