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I am trying to model an open system interaction without making strong assumptions on coupling strength or temperature. In general i understand that open systems are modeled by a Lindbladian, but as far as i know the Lindbladian approximation holds only if we have Marcov, Born and Circular Wave approximation. Since I want to cover a broad range of temperatures and coupling strengths how should i model the bath? Any suggestions on how to proceed?

More specificly a colleague suggested using the coupled harmonic oscillator formalism has the advantage of not making any assumptions apart from being modelable by harmonic oscillators and being analytical solvable! Anyone has recommendations where i can read up how this is done or an opinion if this approach is valid?

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  • $\begingroup$ Are you interested more in the problem of modelling the bath itself satisfactorily or is your aim elsewhere and you just need to use some? If latter, harmonic bath is standard, but beware, it does assume a lot. System of harmonic oscillators can move in a mode, distinguished stable harmonic oscillation, which is hardly expected from general bath. $\endgroup$ – Ján Lalinský Jan 7 '14 at 18:24
  • $\begingroup$ @JánLalinský I am interested in generalizing a model of an open system with interesting behaviour in the weak coupling regime, not the bath itself. Still the systems behaviour can depend strongly on the way the bath is modeled, so i guess i have to take care to do it right. All in all i have to find the right chooice between generality, model independence and solvability. $\endgroup$ – ckrk Jan 8 '14 at 13:07
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Sometimes the bath is taken to be a collection of two-state systems, which is, very roughly, a model of a permanent magnet. Here's an example that comes to mind.

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  • $\begingroup$ Thanks for your answer. Clearly using a collection of two state systems is a viable option in modelling the bath, i am however somewhat concerned how general the model i use is and if i have implicit assumptions in them. To me it is not clear what i have to assume to be sure if i model a bath as i.e. a collection of 2 level system, i am modelling it right! Surely there are other ways to model baths and i have to somehow justify why i am choosing this one, unless i know it is a very general model! $\endgroup$ – ckrk Nov 12 '13 at 23:58
  • $\begingroup$ I don't understand enough (anything) about what you are trying to accomplish, but the definition of thermal equilibrium is that it doesn't matter what you are in equilibrium with. In other words, if you are in equilibrium with bath A and bath A is in equilibrium with bath B, then you are in equilibrium with bath B. However I suspect that it's exactly the nuances of this you are after. $\endgroup$ – lionelbrits Nov 13 '13 at 1:45

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