Derivation of T1 term in Bloch equations

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Discussion Overview

The discussion revolves around the derivation of the T1 term in the Bloch equations, specifically questioning whether it can be rigorously derived without coupling the system to a thermal bath. Participants explore the implications of semiclassical scattering and measurement processes in relation to T1, T2, and decoherence.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants suggest that the contribution of semiclassical scattering to the Bloch equations is typically justified using Fermi's Golden Rule, but question if a rigorous derivation is possible without a thermal bath.
  • Others argue that T1, T2, and T2* are properties of the system in the absence of measurement and are usually associated with coupling to a thermal bath, raising uncertainty about the meaning of T1 without such a bath.
  • One participant points out that the decay of off-diagonal terms in the Bloch equations, attributed to T1, is indeed a form of decoherence, which is typically linked to an environment or bath.
  • Another participant questions the necessity of a bath for deriving scattering rates, suggesting that semiclassical perturbations with random phases might yield similar results.
  • There is a suggestion that some form of environment is needed for the formalism to apply to open systems, and a belief that deriving T1 without an external parameter is not feasible.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of a thermal bath for deriving T1, with some asserting it is essential while others propose alternative approaches. The discussion remains unresolved regarding the derivation of T1 without a bath.

Contextual Notes

Participants highlight the dependence of the discussion on definitions of decoherence and the role of external environments, as well as the implications of semiclassical scattering in the context of open systems.

kcant6453
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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?
 
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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(?).
 
Well, in the Bloch equations T1 is assumed to cause decay of the off-diagonal terms. Isn't that decoherence?
 
kcant6453 said:
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.
.
 
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?
 
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.
 

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