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I recently had to do with a model of a single Spin coupled to a very generic quantum mechanical bath (the actual point was finding pulses that manipulate the spin as accurate as possible despite having a finite length in time but as this doesn't have anything to do with my questions I'll just omit their hamiltonians):

[itex]H = H_b + \vec{\sigma}\vec{A}[/itex]

where [itex]H_b[/itex] describes the internal dynamics of the bath, [itex]\vec{\sigma}[/itex] is the well known pauli matrix-vector and [itex]\vec{A}[/itex] a vector containing operators which model the interaction between the spin (in its 3 directions, of course) and the bath.

In subsequent calculations, it was important not to define either [itex]H_b[/itex] or [itex]\vec{A}[/itex] any further. To remain as generic as possible, even [itex][H_b,\vec{A}] \neq 0[/itex] was assumed, only [itex][\vec{A},\vec{\sigma}] = 0[/itex] was exploited later.

To put it in a nutshell:

I now made up two questions, being

1.is it possible to find a similarly generic model which describes the coupling of the spin to a classical bath and

2. what would a toy model of such a system look like?

Every hint is appreciated.

Thanks in advance!

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# How to model a classical bath?

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