We use the exact solution for the damped harmonic oscillator to discuss some relevant aspects of its open dynamics are often misunderstood. We compare two different approximations both referred to as a rotating wave approximation. Using a specific example, we clarify some issues related to non-Markovian dynamics, non-Lindblad-type dynamics, and positivity of the density matrix.
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Maniscalco et al. (2004) studied this question.
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