Derivation of T1 term in Bloch equations

[kcant6453]

I always see the contribution of semiclassical scattering to the Bloch equations for a two-level system justified heuristically, using Fermi's Golden Rule to calculate the scattering rates. The resulting time evolution of the density matrix is clearly in the Lindblad form, but is it possible to derive this rigorously without coupling the system to some sort of thermal bath? For example, by considering the scattering process to be some sort of measurement?

 

[f95toli]

I am not sure I understand the question. However, T1 (as well as T2 and T2*) are usually assumed to be properties of the system (T1+bath) in the absence of a measurement. Physically the decoherence is -in the simplest case- indeed caused by coupling to a macroscopic thermal bath (or at least something that an be described by a thermal bath).
Hence, I am not even sure what T1 in the absence of a bath would even mean(?). I don't know much about scattering processes (not important in my field), but scattering as such should not result in decoherence(?).

 

[kcant6453]

Well, in the Bloch equations T1 is assumed to cause decay of the off-diagonal terms. Isn't that decoherence?

 

[f95toli]

Well, in the Bloch equations T1 is assumed to cause decay of the off-diagonal terms. Isn't that decoherence?

Yes, indeed (those terms are sometimes called "the coherences"). The decay of those terms is normally due to a bath (or an "environment") of some sort.
.

 

[kcant6453]

Right, but why do you need a bath to get that result? You can derive scattering rates from Fermi's Golden Rule without reference to a bath. For example, could you get the same result by considering a semiclassical perturbation with a random phase?

 

[f95toli]

Well, you need something "other", an environment that you system can couple to meaning whatever formalism you are using it needs to be applicable to open systems.
I have come across Golden Rule calculations for open systems which presumably(?) could be used, is that what you are referring to?

Note that if you are asking if it is possible to somehow derive a value for T1 without referring to a some "external" parameter (e.g. the temperature of an external bath) I do believe the answer is no.